Setup of a Low Temperature Inelastic Light-Scattering System Including Experiments on Topological Materials

Contents

1 Fundamentals of Raman Scattering
1.1 History
1.2 Applications
1.3 Physical Description
1.4 Raman Active Phonon Modes
1.5 Selection Rules for Raman Scattering Experiments
1.6 Experimental Setup
1.6.1 Laser Light-Source

2 Raman Setup for Experiments at Low Temperatures
2.1 KONTI-IT-cryostat Type Spektro 4
2.1.1 General Description
2.1.2 Pumping System
2.1.3 The Interior of the Cryostat
2.1.4 Temperature Control and Regulation
2.1.5 Liquid He-Level Monitor
2.2 KONTI-Cryostat-Mikro
2.2.1 General Description
2.2.2 Temperature Control
2.3 Cryomech PT-405
2.3.1 General Description

3 Theoretical Background on Topological Materials
3.1 Topological Materials in General
3.2 Topological Insulator
3.2.1 Bi2Se3 - 3D Topological Insulator
3.3 3D Dirac Semi-Metal and Weyl Semi-Metal
3.3.1 Electronic Band Structure of Ta As and TaP
3.3.2 ZrSiS - Topological Nodal Semi-Metal
3.3.3 TaAs and TaP - Weyl Semi-Metals

4 Raman Scattering Experiments
4.1 Crystals used for Raman Scattering Experiments
4.2 Experiments
4.2.1 Time Dependence
4.2.2 Orientation and Polarization Dependence
4.2.3 Excitation Energy Dependence
4.2.4 Temperature Dependence
4.2.5 Material Dependence

5 Summary

6 Appendix
6.1 Symmetry Analysis
6.1.1 TaAs and TaP
6.2 Additional Raman Measurements
6.2.1 Neon Lamp
6.2.2 RE123 - High-Temperature Superconducting Cuprates
6.2.3 a-Li₂IrO₃ Iridate with Kitaev Honeycomb Model
6.2.4 TaAs - Temperature Dependent Raman Shift of the Phonon
6.2.5 Antiferromagnetic Compounds Cu₂F₂SeO₃ and CoBi₂O₂F₄

Abstract

The purpose of the experimental investigation was to find the origin of a time dependent Raman scattering signal, which manifests only in certain materials at low temperatures. Within the research group of Prof. Dr. Lemmens, this scattering signal is referred to as the Low Energy Maximum or in short LEM. The name "Maximum" is derived from the peak-shaped form of the scattering data with the highest scattering intensity in the low energy region of the Raman shift as shown in Fig. 1, hence the name "Low Energy".

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Figure 1: Extracts from publications regarding the LEM effect[1],[2].

For some years, the origin of this effect was presumed to be due to a sur­face state of the sample. Dr. Vladimir Gnezdilov has observed and studied this effect on materials, for instance in the giant Rashba semiconductor BiTel and the topological material Bi2Se3. The results have been published[1],[2]. An extract of these papers is illustrated in Fig. 1. Raman spectra with excitation energy dependence, polarization dependence and temperature dependence of the LEM on Bi2Se3 are depicted at the top left and top right, respectively. Time dependent spectra with the evolution of the LEM on Bi2Se3 and BiTel are shown at the bottom left and bottom right, respectively. During the investigations for my bachelor thesis the LEM also appeared on the Weyl semi-metal TaAs and the topological semi-metal TaAs2.

To examine the origin of the LEM, three different cryostats were used to cool the samples. These cooling systems are described in section 2. Various topologi­cal materials and non-topological crystals were examined. The time dependence was investigated over time periods sufficiently long to observe how the LEM develops and/or whether it stagnates after a certain time. Different wavelengths of the laser light have been applied to examine the excitation energy dependence of the LEM. Symmetry analysis on some topological materials has been realized to determine the orientation of the crystals in order to investigate if the LEM is effected by the orientation.

Dr. Vladimir Gnezdilov and Savut jan Sidik, a former PhD student in the research group of Prof. Dr. Lemmens, greatly contributed in gathering Raman data from the materials TaP and ZrSiS.

Überblick

Im Rahmen dieser Masterarbeit soll der Ursprung eines zeitabhängigen Raman- Streusignals untersucht werden, dass sich nur in bestimmten Materialien bei tiefen Temperaturen manifestiert. Dieses Streusignal wird innerhalb der For­schungsgruppe Prof. Dr. Lemmens als Low Energy Maximum oder kurz als LEM bezeichnet. Der Name "Maximum" stammt von der peakartigen Form des Signals. Das LEM befindet sich im Niedrigenergiebereich des Ramanspektrums, so wie es in Fig. 2 abgebildet ist. Daher kommt der Name "Low Energy".

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Figure 2: Auszug von Publikationen über den LEM-Effekt[1],[2].

Es wurde einige Jahre vermutet, dass diesem Effekt ein Oberflächenzustand zugrunde liegt. Dr. Vladimir Gnezdüov hatte diesen Effekt an Materialien wie zum Beispiel am Rashba-Halbleiter BiTel und dem topologischen Isolator Bi2Se3 beobachtet und untersucht. Die Ergebnisse finden sich in Publikationen[1],[2]. Ein Auszug dieser Resultate ist in Fig. 2 illustriert. Oben links beziehungsweise oben rechts ist die Abhängigkeit des LEMs von der Anregungsenergie, der Polarisation und der Temperatur am Beispiel Bi2Se3 gezeigt. Zeitabhängige Spektren mit der Entwicklung des LEMs an Bi2Se3 und BiTel sind unten links beziehungsweise unten rechts zu sehen. Während der Messungen für meine Bachelorarbeit trat das LEM ebenso am Weyl-Halbmetall TaAs und am topolo­gischen Halbmetall TaAs2 auf.

Um der Ursache des LEMs auf den Grund zu gehen, kamen drei unter­schiedliche Kryostaten zum Einsatz um die Proben zu kühlen. Diese Kühlsys­teme sind im Abschnitt 2 beschrieben. Es wurden verschiedene topologische und nicht topologische Materialien untersucht. Die Zeitabhängigkeit des LEMs wurde über eine ausreichend lange Zeit gemessen, um zu beobachten, wie sich das LEM entwickelt und/oder ob die Entwicklung des LEMs nach einer gewissen Zeit stagniert. Es wurde Laserlicht mit verschiedenen Wellenlängen angewen­det, um die Abhängikeit des LEMs von der Anregungsenergie zu untersuchen. Symmetrieanalysen verschiedener topologischer Materialien wurden durchge­führt, um die Orientierung der Kristalle zu bestimmen und so feststellen zu können, ob sich die Orientierung auf das LEM auswirkt.

Dr. Vladimir Gnezdilov und Savut jan Sidik, ein ehemaliger Doktorand der Forschungsgruppe von Prof. Dr. Lemmens, lieferten einen erheblichen Beitrag bei der Aufnahme der Messdaten von TaP und ZrSiS.

Acknowledgements

The support of many people made the experiments for this work possible. I would like to thank Prof. Dr. Peter Lemmens, who gave me the opportunity to realize these investigations and his permission to setup a new cooling system for the experiments. I am also very thankful for the interesting discussions during group meetings and in general. Without his engaged support this work would not have been possible.

I would like to give my thanks to Dr. Vladimir Gnezdilov and Dr. Oleksandr Glamazda, who made every endeavor to pass on their knowledge about the ex­perimental part, for their excellent explanations and demonstrations on how to operate different cooling systems, how to work with optics and its adjustments and how to tackle delicate situations that might arise during a Raman scatter­ing experiment. Dr. Azat Sharafeev has always been very generous in sharing his experience on Raman scattering and gave appropriate advices for trouble­shooting. I appreciate the support of Dr. Dirk Wulferding during the final stage on the thesis.

I express my gratitude to those who assisted in setting up and maintaining the required appliances for the experiments, Thilo Lampe, Arno Ellermann, Lutz Nagatz and Dana Schulte genannt Berthold.

It was a pleasure to work together with Savutjan Sidik, who worked with great engagement, even during weekends. Members of the reseach group, Prof. Dr. Samir Kumar Pal, Bo Liu, Florian Biischer, Daniel Schmid and Andreas Reutter, have always been attentive for discussions about physics and I thank them for it very much.

I would like to thank Dr. Dirk Menzel for his valuable contribution on giv­ing a possible explanation of the LEM effect and his effort in passing physical knowledge not only to me but to all other students in his lectures.

I am grateful to my partner Janosch Meier and my mother Maria Milliner for their loving and caring support. I thank Kim Paul Schmidt for our fruitful dis­cussion about physics related to this topic and beyond.

Prof. Dr. Litt erst taught US how to realize scientific work. Without his advices during his lectures, this investigation might have been realized in a different manner. His statement "the law of physics apply anywhere in the world and not only in one room", and "a new phenomenon should always be tested in another system because the laws of physics apply everywhere", motivated to realize experiments in different systems.

Chapter 1

Fundamentals of Raman Scattering

1.1 History

The Austrian physicist A. Smekal had theoretically predicted the inelastic light­scattering effect in 1923. Two scientific groups independently observed this effect experimentally shortly thereafter.

In India, a student of Prof. c. V. Raman noticed in the early 1920's, that the scattered light from liquids showed components of different wavelength compared to the incident light. He observed this by using various color fil­ters. For the following years the research group of the Indian scientist Sir c. V. Raman thought that fluorescence was its origin. However, Sir c. V. Raman (see Fig. 1.1) and K. s. Krishnan later concluded that fluorescence is improbable to be the cause, because of the polarization characteristics of the scattered light. In general, fluorescent light is unpolarized, but they had observed scattered light which was polarized. Due to the polarized light characteristics after the scattering process, the group theorized that this type of light-scattering could be similar to Rayleigh scattering, with the difference that this was inelastically scattered light. On March 16, 1928, Sir c. V. Raman gave his first public lecture about their new findings with the title "A New Radiation" and he published his research[3]. Together with his research group, he developed a setup with monochromatic polarized light to prove the inelastic light-scattering process. They achieved to develop this setup and were able to observed color lines that differed from the incident light after being scattered. They also demonstrated this in public.

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Figure 1.1: Sir c. V. Raman in his laboratory with one of his inelastic light­scattering setups[4].

In 1929, C. V. Raman and K. s. Krishnan photographed the inelastic com­ponents of a mercury arc after the interaction with liquid tetrachloride (see emission spectrum in Fig. 1.2 (b)). The emission spectrum of the monochro­matic light-source (mercury arc with a wavelength of A = 435.83 nm ) is shown in Fig.1.2 (a). The intensity of the scattered light as a function of frequency is illustrated in (c)[3]. In 1930, Sir c. V. Raman was awarded with the Nobel Prize in Physics.

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Figure 1.2: (a) Emission spectrum of a mercury arc. (b) Spectra of liquid carbon tetrachloride excited by the mercury arc radiation, (c) Scattering intensity as a function of frequency[3].

In a similar time period, two scientists from the Soviet Unhon, G. Landsberg and L. Mandelstam, had also observed the inelastic light-scattering effect in quartz crystals.

1.2 Applications

Nowadays, Raman scattering experiments are used in many branches of science, for instance in

- industry
- biology
- material science
- chemistry

Each compound and element has its own fingerprint of vibrational modes also known as phonons. Therefore, this technique enables the determination of ma­terials and their composition. Heavy elements have a low energy shift relative to the incident excitation energy This energy shift is referred to as the Raman shift. On the other hand, lighter elements have a greater Raman shift. A sym­metry analysis of a crystal is possible due to the selectivity of the polarization of the incident and scattered light. The resonant energy of the phonons or other quasi-particle excitation can also be deduced by applying different laser exci­tation energies. Additionally, high-temperature superconducting cuprates are investigated with Raman scattering experiments. They produce Raman spectra with a broad scattering signal at approximately 2000 cm-[1]. This is referred to as two-magnon scattering. Examples of two-magnon scattering are demonstrated in section 6.2.2. The magnetic exchange interaction can be derived from the Raman shift. Phase transitions of magnetic ordering can also be monitored by Raman scattering experiments. In these type of experiments, an additional mode usually appears below a certain critical temperature.

Raman spectroscopy is a very powerful and useful tool for scientific research, because it not only allows solids to be examined but also liquids, molecules and even gaseous materials. Provided that the laser light power is not too intensive, the Raman scattering is a non-destructive and non-invasive method, i. e. the sample is not damaged during the examination process and can be reused for experiments.

1.3 Physical Description

Raman spectroscopy analyzes inelastically scattered light. The light is scat­tered from quasi-particles. These include, for instance, lattice vibrations in the crystal (phonons). Optical phonons are most commonly investigated. Other quasi-particles are magnons, plasmons and electronic excitations[5].

When an electromagnetic (EM) field E(co) is applied on a sample that has a polarizability of a0, a dipole moment is created:

PD(a>) = α0Ε(ω) (1.1)

Equation 1.1 describes the case for an evanescing EM wave. If the vibration of the molecule oscillates with the frequency Ω, the atomic distance alters periodically between the atoms A and B, resulting in a modulation of the polarizability The total dipole moment then yields:

PD(a>) = («0 + «1 cos Ωγ)Ε0 cos cot (1.2)

Application of trigonometric sum rules yields:

PD(a>) = a0E0cos cot + (a!E0/2)[cos(a> + Ω)Γ + cos(a) - Ω)Γ] (1.3)

Equation 1.3 describes an EM wave that oscillates with ω ± Ω, where ω is the visible light in the order of 20,000 cm-[1]and a sideband (vibrational mode) Ω with the order of a few cm[1]־ to a few hundred cm[1]־.

Quantum-mechanically, the light-scattering process is described by the conser­vation of energy and momentum as illustrated in Fig. 1.3.

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Figure 1.3: (left) Scheme of the energy levels in the Raman scattering process with the initial state i, an intermediate/excited state z and the final state f. (right) Conservation of momentum in the Raman scattering process[5].

Mathematically, this can be described as

Ha>i = Hcos ± Ю (1.4)

Hki = Hks ± Hq (1.5)

where ú)i and cos represent the frequency of the incident and scattered light, respectively The wave vectors for the incident light, scattered light and the phonon are denoted by ki, ks and q, respectively When the scattered light is of lower frequency than the incident light, Hiúi > HcOs, a phonon is generated. This is called Stokes Raman scattering and analog to a red-shift. When a Stokes Raman scattering process occurs, an anti-Stokes Raman scattering process also appears with the same displacement but to a higher frequency with respect to the frequency of the incident light, %ú)i < H(JŮS. This is analog to a blue-shift. These scattering processes are illustrated in Fig. 1.2. Anti-Stokes scattering is of weaker intensity than the Stokes scattering. The Raman scattering process is in effect when there is a probability of transition and decreases with increasing temperatures.

In general, cm-[1]is used to describe the Raman shift. However, sometimes it is favorable to use a different energy scale, for instance

1 cm0.125 »[1]־ meV « 1.4 к « 33 GHz (1.6)

When nuclei vibrate about their equilibrium position Q, an alternation of the polarizability a is induced. This can be expressed by expanding each component αρσ (Taylor series) with the polarizability at equilibrium configuration (aPo)0 and the normal coor­dinates Qk;u

1.4 Raman Active Phonon Modes

The phonon is Raman active if it undergoes a change in polarizability dapo with the change of the normal coordinates dQk upon an oscillating incident EM field. Mathematically, this is expressed as and can be thought of a mechanical deformation of the unit cell in a crystal or a molecule. Fig. 1.4 and 1.5 show molecules with different constellations and vibrations of the atoms A and B. The modulation of a and PD in the vicinity of the equilibrium position Q determines whether the mode is Raman and/or infrared active[6].

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Figure 1.4: Different alignments of molecules with the atoms A and B. It shows the displacement of the atoms and illustrates when the mode is Raman and/or infrared active[6].

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Figure 1.5: Different vibration modes for the shown molecule with an illustration when the mode is Raman and/or infrared active[6].

1.5 Selection Rules for Raman Scattering Experiments

The scattering intensity can be determined with the polarization vector of the incident light g;, the scattered light es and the Raman-tensor Ri as followed

I°c\et-Rt-es\[2](1.9)

The Raman-tensor varies with the space group of the crystal. It holds in­formation of whether a mode is Raman active or not. Additionally, Ri shows in which polarization the modes become Raman active. This is referred to as selection rules. Section 6.1 gives an example on how the orientation of the crystals TaAs and TaP is determined by the application of selection rules. Table 1.1 shows the orientation of the polarization vectors.

Table 1.1: Polarization vectors for different polarized light. A scheme of the orientation of these vectors are depicted in Fig. 1.6.

To visualize the polarization vectors, Fig. 1.6 sketches these polarization vectors on the example of a CuO-plane. The prime after the X indicates a 45° rotation in the xy-plane as shown in the Figure. The first and second letter represents the polarization of the incident and scattered light, respectively R and F indicates circular polarized light with a rotating polarization vector in time. R corresponds to a right-handed circulation in the moving direction and F to a left-handed circulation. In the following, Raman data the polarizations are depicted in italic, bold and without parenthesis, for example YX. Raman data in the appendix sometimes show an и which corresponds to unfiltered light, i. e. a polarization filter is not applied.

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Figure 1.6: Polarization of incident and scattered light on the example of a CuO-plane[7].

1.6 Experimental Setup

Raman Scattering is a branch of spectroscopy. It requires light as an excitation source, optical parts, light-matter interaction, a spectrometer to analyze the scattered light and a detector to record the spectral information.

Fig. 1.7 illustrates a typical Raman scattering setup. The light from the laser is indicated with the green line. Monochromatic light, coherent in phase and propagation is favorable and commonly applied. The polarization of the light is adjustable before the interaction with the sample. The same holds true for the scattered light. Optionally, the polarization filters can be removed. For a good quality of the Raman spectra, the sample is commonly placed in a cryogenic vacuum environment. For the experiments, two different inelastic light-scattering setups were used:

- Modular XY system from Dilor
- HR 800 from HORIBA Jobin Yvon

In the Modular XY system, the laser beam incites the sample, that is attached on the sample-holder, from an angle of about 30°. Approximately 5 cm in front of the sample, the scattered light is collected and collimated with a lens before entering the spectrometer. This setup is commonly known as macro-Raman and is depicted in Fig. 1.7. The HR 800 setup operates in a different way The incident and scattered light passes through the same microscope objective, hence this setup is often referred to as micro-Raman. The focusing of the laser-light is achieved through the microscope. Therefore, the name confocal microscopy is often used. A notch filter suppresses the elastically scattered light, the Rayleigh scattering.

1.6.1 Laser Light-Source

Various laser light-sources may be applied. The COHERENT®C0mpass 315M- 100 (compact all solid state lasers) is frequently used for our experiments. It is a diode-pumped Nd:YAG laser (Neodymium-doped Yttrium-Aluminum-Garnet- Faser) and emits light at a wavelength of Aexc = 532.1 nm[8]. Another laser used is the plasma tube Ar-Kr ion laser, COHERENT® Innova 70 Spektrum. Ion laser produce a great number of multi-line laser-light simultaneously. These can either be separated with an external prism or another dispersive element inside the laser[9]. In our experiments the latter mentioned configuration is used.

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Figure 1.7: (top) Photo of the macro-Raman setup, (bottom) Scheme of the above photo with a description of its main components[10].

Chapter 2 Raman Setup for Experiments at Low Temperatures

A Raman spectrum taken from a sample exposed to air shows many additional modes in the low energy region of the Raman shift. These modes do not originate from the sample. Temperature also influences the Raman spectra significantly. In general, the scattering intensity of a phonon increases and its line-width reduces with decreasing temperatures. At low temperature numerous materials harbor phase transitions, for instance magnetic ordering below a certain critical temperature. These phase transitions can be monitored by Raman spectroscopy. It is therefore essential to use a cryogenic vacuum environment (often referred to as cooling system) for the samples during Raman experiments. For this work, three different cooling systems were used:

- KONTI-IT-cryostat type Spektro 4 (see section 2.1)
- KONTI-cryostat-Mikro (see section 2.2)
- Cryomech PT-405 (see section 2.3)

KONTI-cryostats are continuous-flow cryostats and use Helium (He) as a cryo­genic cooling agent. The flow of liquid Helium (LHe) from the Не-tank is adjustable and consequently the temperature inside the sample chamber. The vaporised cryogenic fluid is pumped through the sample chamber by a vac­uum pump. The KONTI-IT-cryostat type Spektro 4 can additionally operate as a Не-bath cryostat where the sample chamber can optionally be filled with LHe.

The Cryomech PT-405 cryostat is a cold-head, pulse-tube cooler and also referred to as closed-cycle cryostat. The samples inside this cryostat are situated in vacuum and cooled via an attached metallic cold-plate that connects to the sample-holder. Therefore, the sample holder is sometimes referred to as cold- finger. The metallic cold-plate serves as a thermal conductor between the helium vapor chamber and the sample chamber.

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Table 2.1: Advantages and disadvantages of the KONTI-IT Spektro 4, KONTI- cryostat-Mikro and Cryomech PT-405 cryostat.

2.1 KONTI-IT-cryostat Type spektro 4

2.1.1 General Description

KONTI-IT-cryostats are produced by the CryoVac Gesellschaft für Tieftempera­turtechnik GmbH & Co KG and are partly made of stainless steel. They can be operated as a helium-bath cryostat or a continuous-flow cryostat. The temperature in the sample compartment is variable between 1.2 - 325 K. The system has an integrated liquid helium-Tank (LHe-tank) and liquid nitrogen­tank (LN2-tank) as shown in 2.6. The integrated heat exchanger permits the LHe or He gas to flood the sample compartment via a sintered diffusor (see Fig. 2.2). The sample holder is inserted from the top, hence the name "top loading . Fig. 2.1 sketches the setup for this type of cryostat. A descriptive photo of the entire setup is shown in Fig. 2.3.

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Figure 2.2: Sample compartment of KONTI-IT-cryostat type Spektro 4. The sintered diffusor optimizes the cooling efficiency (gray area at the bottom). The golden-colored round plate inside the cryostat is the sample holder.

The cryostat is suitable for uv, IR and Raman spectroscopy with the follow­ing features:

- low refrigerant usage
- high cooling efficiency due to the sintered diffusor and contact gas
- short cooling time of approximately one hour
- flanged windows - different window materials possible
- sample holder can be rotated in zy-plane and around z-axis
- homogeneous cooling of the sample and its environment
- cooling below the temperature of LHe possible

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Figure 2.3: Photo of the setup with the KONTI-IT-cryostat type Spektro 4. (1) He-transfer line. (2) Cryostat. (3) He-vessel. (4) & (5) Vacuum pumps. (6) Heater and temperature control. (7) LHe-level monitor.

2.1.2 Pumping System

Two pumps are necessary to operate the KONTI-IT-cryostat type Spektro 4 at low temperatures. One pump exhausts air from the insulating vacuum layer (4 in Fig 2.3). The other vacuum pump is connected to the sample compartment (5 in Fig 2.3).

The right side of Fig. 2.4 displays the front view of pump 4 in Fig. 2.3. This system is responsible for the insulating vacuum (see green arrows). The pump is composed of a pre-vacuum pump and a turbo-pump that generates a pressure of « 4.0 X IO-[7]mbar. The upper part of the cryostat with the connection to the sample chamber and the insulating vacuum is shown on the left side of Fig. 2.4. pressure seen in this photo) pre-vacuum pump

Figure 2.4: (left) Photo from the top part of the KONTI-IT-cryostat type Spektro 4 with two connections to the vacuum system, (right) Vacuum system for the insulating vacuum.

Insulating vacuum needs to be generated prior to the filling of LN2 into the LN2-tank. Otherwise, the LN2 would evaporate quickly from the tank and fill­ing of LHe into the Не-tank would be inhibited. Outer freezing is avoided by the insulating vacuum.

The other pump (5 in Fig. 2.3) has two purposes. In the initiating stage air is evacuated from the Не-tank. Afterwards, the Не-tank is flooded with He gas (see lilac arrow in Fig. 2.5). This prevents freezing of tubes inside the cryostat when LHe is filled into the Не-tank. The second purpose is to evacuates the sample compartment from air and evaporated He gas during low temperature operations. This pump consists of a pre-vacuum pump and does not generate very high vacuum. During cold temperature operation, a pressure of approx­imately 1 mbar is maintained inside the sample compartment. It is connected to two exits, the He-exhausts, which leads the evaporated He gas to the He- recovery system and an air exhaust. The He-recovery system reliquefies the collected He gas for later reuse.

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Figure 2.5: (left) Top part of the cryostat with the connection to the Не-tank (lilac arrow), (right) Vacuum system for the Не-tank and the sample chamber.

2.1.3 The Interior of the Cryostat

Fig. 2.6 shows a photo of the KONTI-IT-cryostat type Spektro 4 together with a detailed sketch of its interior. The cryostat is composed of the following layers:

- insulating vacuum (light-green region in Fig. 2.6)
- N2-tank (yellow region in Fig. 2.6)
- Не-tank (pastel-green region in Fig. 2.6)
- sample room area (white central region in Fig. 2.6)

The sample compartment is the central lower area of the cryostat. It is also known as sample area, sample room or sample chamber. The sample is placed on a sample holder which is inserted from the top of the cryostat into the sample space filled with He gas. Air is extracted from the outermost layer of the cryostat (see light-green shaded area of Fig 2.6). This air-extracted area is referred to as the insulating vacuum because it protects the inner layers from environmental temperatures.

In order to avoid high temperature gradients in the sample room area, cop­per is the prime material in its surroundings. A radiation shield between the sample chamber and the Не-tank prevents heat loss in the central area during operation at higher temperatures.

This cooling system is equipped with a heater at the bottom of the sample chamber and a temperature controller. The temperature may be selectively varied between 1.4 к and 325 K. The amount of He gas pumped from the sample chamber is controlled by a valve which is connected to the LHe reservoir via a cold needle. The temperature is regulated in this manner. The LN2 is transferred from a N2-vessel through a flexible hose and is filled approximately every twelve hours. After one day of the first filling of LN2, a temperature of « 105 к is reached in the sample compartment. Upon reaching this temperature, LHe may be filled into the He-tank.

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Figure 2.6: (left) The interior of the KONTI-IT-cryostat type Spektro 4 with the layers: N2־tank in yellow, the vacuum chambers in light-green and the He-tank in pastel green[11]. (right) Photo of the cryostat. Paper tissues at the top of the cryostat to absorb condensed water and thereby prevent refreezing during refill of I.N2·

2.1.4 Temperature Control and Regulation

The temperature inside the sample compartment is monitored and regulated by the TIC 304-MA temperature controller, shown in Fig. 2.7 (manufactured by CryoVac, Germany). This device can be used for different cryostats, however, it is particularly designed for KONTI-IT-cryostats.

A Si-diode interprets the temperature inside the sample compartment. Both, the heating voltage and the electric current for the heating is adjustable from 0 -40 V DC, and 0 - 1.5 A, respectively The heating power has a maximum value of pmax = 60 w.

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Figure 2.7: Temperature controller TIC 304-MA used for monitoring and regu­lating the temperature inside the sample compartment.

2.1.5 Liquid He-Level Monitor

AMI - Model 135 Helium-level monitor (made by American Magnetics, USA) is used to register the He-level inside the Не-tank. A photo is depicted in Fig. 2.8.

The resistance of the superconducting level sensor inside the Не-tank be­comes superconducting along the part where it touches LHe. Hence, the resis­tance practically disappears in this region. The LHe-level inside the He-tank can thus be deducted by a resistance measurement of the total length of level sensor. The resistivity is converted into percentage of the hight of LHe inside the Не-tank. The sensor current lies at 75 mA.

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Figure 2.8: A He-level monitor (AMI Model 135 Liquid Helium-Level Monitor) registers the He-level in the Не-tank. The number on the display provides the percentage of the LHe-level inside the He-tank.

2.2 KONTI-Cryostat-Mikro

2.2.1 General Description

The KONTI-cryostat-Mikro is a continuous-flow cryostat produced by CryoVac Gesellschaft für Tieftemperaturtechnik GmbH & Co KG. A sketch of the interior is illustrated in Fig. 2.9.

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Figure 2.9: Scheme of the KONTI-cryostat-Mikro with its components[12].

This type of cryostat is utilized in micro spectroscopy and Raman spectroscopy. It has the following characteristics:

- easy to handle due to its compact design (no built-in He reservoir)
- fast cooling of approximately one hour
- ranged between 3.5 - 325 к
- windows of optical quartz
- He supplied from a He-vessel via a tube line
- low electrical power consumption

A general view of the KONTI-cryostat-Micro setup is shown in Fig. 2.10 with the connections to the vacuum pumps, helium supply and temperature monitoring/regulating system.

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Figure 2.10: Overview of the KONTI-cryostat-Mikro setup. (1) Vacuum pump for the sample chamber. (2) He exhaust pump. (3) Movable X/Y table. (4) Cryo­stat. (5) Microscope. (6) Connection to the temperature regulation/monitoring. (7) Connection to the He-transfer line.

2.2.2 Temperature Control

The same type of temperature controller is used as for the KONTI-IT-cryostat type Spektro 4 (see section 2.1.4).

2.3 Cryomech PT-405

2.3.1 General Description

The Cryomech PT-405 is a two-stage closed-cycle pulsed tube (PT) cryocooler built by Oxford instruments. Helium circles between the water-cooled compres­sor package (CP) and the cold-head via two tubes. Thus, a refill of LHe is not required during operation at low temperature. A system drawing is shown in Fig. 2.11.

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Figure 2.11: Cryorefrigerator system - Cryomech PT-405. (left to right) Compressor package (CP), connection tubes for the circulation of Helium, cold-head [13].

Applications of this type of cooling system include uv, IR, Rama and visible spectroscopy as well as photoluminescence[14]with the following features:

- long mean-time between maintenance
- fast cooling (60 min. to cool from room temperature to 4.2 K)
- temperature range between 2.7 - 325 к
- sample in vacuum environment
- water cooled compressor package
- continuous period of operating time at low temperature

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Figure 2.12: (left) Photo of the Cryomech PT-405 system[14]. (right) Sketch of its interior of the cooling system with the cooling stages.

Helium gas circles with a continuous flow. Its flow is regulated by a needle valve. There are two modes of operation, the "pull" mode and the "push" mode. In the pull mode, the cryostat draws He gas from a storage dewar in the CP to the heat exchanger. It thereby uses an oil-free pump. This mode has the advantage of not having to monitor the storage dewar pressure. The push mode pushes He gas trough the heat exchanger by pressurizing the storage vessel. It is used if the vibration and/or noise from the pump is inconvenient.

Chapter 3

Theoretical Background on Topological Materials

3.1 Topological Materials in General

William Thomson, also known as Lord Kelvin (1824-1907) imagined that atoms are discrete and immutable. He believed that matter can be merely described by its topology and that geometry does not matter. His theories were based on his observations of the smoke rings, which are stable in air for a fair amount of time while traveling through air. With his assumption, he introduced knot invariants, which are distinct for each atom. An example of these knot invariants for carbon, oxygen and hydrogen after his modes is illustrated in Fig. 3.1. The name topological matter derives from his definition of topologically ordered matter.

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Figure 3.1: Lord Kelvin's idea was that each atom has its own topology and geometry does not matter[15].

Topological materials are a class of solids with electronic states governed by symmetry considerations that are invariant under topological transformations. Hence, the dispersion of electronic states or the existence of surface states are in­dependent of defects. Properties of topological materials indicate the existence of exotic quasi-particles, like Majorana-, Weyl- and Dirac-fermions. Many of the discussed materials have an extremely large electronic mobility or magnetic field dependent resistivity This makes them attractive for possible applications in electronics.

There are several classes of topological materials, for example: topological insulators, topological Weyl semi-metals and topological Dirac semi-metals.

3.2 Topological Insulator

A topological insulator (TI) is a material with an electronic band gap in its bulk (insulator). On its surface the electronic bands are characterized by linear dis­persion bands that touch at certain points. There are 3D TI and 2D TI. The study of TI was inspired by their robustness to scattering of conducting edge states in quantum Hall systems [16]. Bi2Se3 is an example of a TI. Fig. 3.2 presents the elec- tronie structure of an insulator and different systems of topological insulators.

Fig. 3.2 (a) depicts an insulator where the energy gap separates the occupied and empty electronic states. The quantum Hall effect (QHE), with electrons moving in circle around applied magnetic field, is illustrated in Fig. 3.2 (b). The motion of electrons is interrupted on the boundary of the sample, leading to a conducting surface along one direction of the edge.

Fig. 3.2 (c) represents the Quantum spin Hall effect (QSHE) or 2D TI in which the boundary contains left and right moving electrons with opposite spins (spin-up and spin-down) propagating in opposite directions. Electrons can move freely in any direction in a 3D TI (shown in Fig. 3.2 (d)). The traveling direction of the electron determines its spin and vice versa. The 2D energy-momentum has a similar Dirac cone to graphene.

3.2.1 Bi2Se3 3־D Topological Insulator

Bi2Se3 has a rhombohedral unit cell with the space group D53d (R3rn). Fig. 3.3 illustrates the crystal structure of Bi2Se3 with the primitive lattice vectors t]3׳2׳. It hosts five atoms per unit cell and has layered structures with a triangle lattice in one layer. The five atomic layers along the z-direction are denoted as quintuple layer (see red rectangular in Fig. 3.3).

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Figure 3.3: (left) Crystal structure of Bi2Se3 with three primitive lattice vectors t!3׳2׳. One quintuple layer is indicated by the red square, (a) ARPES measure­ments of the surface band dispersion of electronic states with a spin-polarized Dirac cone, (b) Chiral left-handed spin textures on the Fermi surface, (c) Scheme of the surface and bulk band topology, (d) A spin-polarized Dirac fermion on the surface of Bi2Se3[16],[18].

Theoretical calculation of the band structure of this compound predicts an energy gap of Eq = 0.3 eV. The topological surface states harbor a single gapless Dirac cone in the momentum space point of the Brillouin zone к = о г[16].

The Dirac cone near the г point of the surface Brillouin zone has been exper­imentally detected with angle-resolved photoemission spectroscopy (ARPES) on Bi2Se3 as shown in Fig. 3.3[19].

3.3 3D Dirac Semi-Metal and Weyl Semi-Metal

3D Dirac Semi-metals (DSM) host two sets of linear, doubly degenerate bands and cross at a fourfold degenerate crossing point, the Dirac point, also known as Dirac node. It is the touching point between the valence and conduction band (VB & CB) and lies near the Fermi energy Ep. DSM can be thought of a 3D ana­logue of graphene. The Dirac state is protected by inversion and time-reversal symmetry. If one of them is broken, the double degenerate bands split and form a single degenerate band. The degeneracy at the Dirac node is then lifted from four-fold to two-fold. These crossing points are denoted as Weyl points (WP) and are also called Weyl nodes. They act as magnetic monopoles in momentum space and come in pairs. The Berry flux is a result of these monopoles. These materials are denoted as Weyl semi-metal (WSM). NbP, TaP, NbAs, and TaAs are examples of WSM. Cd3As2, Na3Bi and ZrSiS are 3D DSM whereas the latter compound is also referred to as a topological nodal semi-metal[20].

Due to the linear dispersion relation, the electrons are massless and behave like relativistic particles with a velocity approximately 300 times less than the speed of light[21].

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Figure 3.4: (left) 3D DSM hosts two sets of Dirac points with doubly degenerate bands, (right) Electronic band dispersions of a WSM with one pair of WP. The arrows pointing inward and outward around the cone indicate magnetic monopoles that result in the Berry flux[20].

3.3.1 Electronic Band Structure of TaAs and TaP

The electronic band structure of the Weyl semi-metals TaAs and TaP is depicted in Fig. 3.5. (a) Shows the Brillouin zone with an energy ranging from -8 to +2 eV from the Fermi energy together with the calculated bands of TaAs. An enlarged view of the WP is illustrated in (b). The occupation probability of the electronic states for different temperatures is sketched in (c) and a comparison of the WPs of TaAs and TaP is depicted in (d).

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Figure 3.5: (a, b) Band structure of TaAs[22]. (c) Probability of electronic states at the vicinity of the WP points in TaAs shaded in blue[23]. (d) WP of TaAs and TaP[24].

3.3.2 ZrSiS - Topological Nodal Semi-Metal

ZrSiS is a non-toxic earth-abundant material making it very attractive for pos­sible future applications. Similar to other Dirac materials, its band dispersion is linear at the touching point between the VB and CB and the bands are described by Dirac cones. In contrast to other Dirac materials, the energy level of the crossing points of the linearly dispersed bands is much higher than in any other known Dirac material. It can reach 2 eV above and below Ep[25].

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Figure 3.6: (left) Crystal structure of ZrSiS. (right) ARPES data of ZrSiS showing the linear band dispersion. The photo energy applied was 50 eV at 20 K.

ZrSiS crystallizes in a tetragonal structure and belongs to the space group P4/nmm (no. 129)[26],[27]. The left panel of Fig. 3.6 provides the crystal structure of ZrSiS[25]. The blue cuboid indicates the square Si net unit cell.

ARPES measurements have confirmed the existence of multiple Fermi pock­ets. Fig. 3.6 (middle and right panel) depicts ARPES measurements on ZrSiS with an incident photon energy of 50 eV at 20 K. The linearly dispersive surface states are in the vicinity of £| and are shown along the high-symmetry direc­tion ΓΧ and ΜΓΜ. The data deliver the topological Dirac line node semi-metal phase. Since there are no other band interferes at the Fermi level, this electronic structure is a candidate for Dirac physics[25],[28].

3.3.3 TaAs and TaP־Weyl Semi-Metals

The first reported topological WSM state was reported in July, 2015 with ARPES measurements on TaAs[29]. Shortly thereafter, this has also been confirmed for TaP[30]. TaAs and TaP have the same body-centered, tetragonal, non- centrosymmtric structure with the space group /41 má as shown in Fig. 3.7. The lattice parameter differs between the two compounds and the element p replaces the element As. Their atomic parameters are shown in table 3.1.

In WSMs either time-reversal or the inversion symmetry is broken. In TaAs and TaAs it is the inversion symmetry that is broken.

Figure 3.7: TaAs: (a) Crystal structure of the unit cell, (b) First Brillouin zone[24]

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Table 3.1: Fattice parameters of TaAs and TaP[24],[31].

Chapter 4

Raman Scattering Experiments

4.1 Crystals used for Raman Scattering Experiments

The following topological materials were investigated in Raman scattering experiments. More information on these materials can be found in section 3. Some of the samples are shown in Fig. 4.1:

- Ta As, TaAs2/ TaP, ZrSiS

The Raman scattering data are compared with Raman data of two other topo­logical materials that had previously been investigated by other research group members of Prof. Lemmens:

- Bi2Se2, Cuo.7Bi2Se3

The two non-topological materials were examined in order to compare the data with the non-topological materials:

- CaF2/ Si

These non-topological materials are depicted in Fig. 4.2.

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Figure 4.1: Some of the topological materials used in the Raman scattering experiments. TaAs has been investigated in (100) and (001) orientation. The scale at the lower right corner holds true for the shown samples.

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Figure 4.2: (left) CaF2 and paper with millimeter scale at the bottom, (right) Si.

4.2 Experiments

The LEM has been recorded in Raman data originating from samples that were cooled with the Cryomech PT-405 cryostat. The other two cryostats used for the measurements (KONTI-IT-cryostat type Spektro 4 and KONTI-cryostat-Mikro) do not show this effect. Details about these cryostats can be found in section 2. This section compares and discusses the collected Raman data of the time depen­dence of the LEM, orientation dependence of the sample, laser excitation energy dependence, temperature dependence and material dependence on the LEM.

4.2.1 Time Dependence

Raman data of TaP, ZrSiS and Ta As with an excitation energy of A exc = 532.1 nm are presented in this section. ZrSiS has been measured by Sainitjan Sidik, TaP by Dr. Vladimir Gnezdilov and TaAs by myself. The polarization, excitation energy and time at the given temperature is shown in the corresponding graphs.

Raman data of TaP cooled with the Cryomech PT-405 and KONTI-cryostat- Mikro are compared in Fig. 4.3.

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Figure 4.3: (left) Time dependent Raman spectra of TaP cooled inside the Cry- omech PT-405 cryostat, (right) The same TaP crystal cooled inside the KONTI- cryostat-Mikro.

After approximately 15 hours at 9 к the Raman spectra shows the distinct line shape of the LEM, where the sample was cooled in the Cryomech PT-405 cryostat (Fig. 4.3 left panel). The LEM after 144 hours at 8 к is fitted with a Gaussian curve and has its maximum at 38.4 cm-[1]. In contrast, no LEM devel­ops when the sample is cooled inside the KONTI-cryostat-Mikro.

A similar behavior is observed in ZrSiS. The crystal cooled inside the Cry- omech PT-405 cryostat exhibits a time dependent Raman spectrum with the evolution of the LEM (left panel in Fig. 4.4). After 102 hours at 8 к the spectrum is fitted with a Gaussian curve. It has its maximum at 41.1 cm-[1]. Inside the KONTI-cryostat-Mikro the Raman data of same crystal show no time depen­dence (right panel in Fig. 4.4). The KONTI-cryostat-Mikro uses a notch filter which gradually starts to suppress light-scattering below 100 cm[1]־ and fully filters scattered light below 50 cm[1]־. The LEM, develops below «130 cm[1]־.

Fig. 4.5 provides the Raman spectra of TaAs measured in the Cryomech PT-405 cryostat. The spectra show a time dependent development of the LEM. After 15 hours at 10 K, a distinct elevation of the spectrum is observed in the low energy region. A Gaussian fit is shown in the spectrum at 206 hours and fits the shape of the LEM.

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Figure 4.5: Time dependent Raman spectra of TaAs. The sample was cooled inside the Cryomech PT-405 cryostat.

Fig. 4.6 compares Raman scattering measurement on TaAs in two different cryostats and in two different orientations. The left panel depicts TaAs cooled in the Cryomech PT-405 cryostat with a time dependent development of the ТЕМ. At 125 hours the ТЕМ of the spectrum is fitted with a Gaussian curve. The middle and right panel illustrate spectra that originate from TaAs cooled inside the KONTI-IT-crostat type Spektro 4 (Не-Bath cryostat). In this cryostat, neither plane of the crystal exhibits an evolution of a LEM over time.

In order to verify if the LEM is a "one-time-effect", the TaAs crystal in (001) orientation that showed no time dependent spectrum in the KONTI-cryostat- Mikro, was subsequently measured in the Cryomech PT-405 cryostat, where the effect reappeares. This data are presented in Fig. 4.7.

Discussion

Fig. 4.8 illustrates the integrated scattering intensity of the LEM from the Raman data shown in Fig. 4.6, Fig. 4.5, Fig. 4.4 and Fig. 4.3. In approximation, the LEM increases at a steady rate for a certain time. After 140 ± 10 hours at low temper­ature, the integrated intensity of the LEM stagnates to increase.

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Figure 4.8: Integrated intensity of the LEM over time in TaAs, TaP and ZrSiS.

The prolonged time scale for the LEM to develop to its full extent is an in­dication that the effect is not intrinsic. A change of the band structure of Bi2Se3 has been reported in ARPES measurements over a time period of two hours at 100 К[32]. Due to the absence of the LEM at 100 K, the data do not quite reflect the LEM in our data. Moreover, the time scale of nearly one week for the LEM to develop fully is rather extensive.

Another observation proposes that the effect is not intrinsic. It is the ob­servation of an icy condensate which crystallizes on certain surfaces at low temperatures inside the Cryomech PT-405 cryostat. The condensation can be observed by placing a magnifying glass in front of the sample. On Si and CaF2 the icy condensation has not been detected in the Cryomech PT-405 cryostat at low temperatures and from these materials a LEM has not been recorded in our data. More about material dependence of the LEM is found in section 4.2.5. Inside the two KONTI-cryostats, the icy condensation has not been observed on surfaces of the samples during cold temperature measurements time. The fact that the choice of the cryostat decides whether the LEM appears, implies that the effect is not of intrinsic nature.

4.2.2 Orientation and Polarization Dependence

Raman spectra of TaAs in (100) and (001) orientation with different polarization settings are provided in Fig. 4.9. The samples were cooled inside the Cryomech PT-405 cryostat. The percentage given in the graphs represent the integrated intensity of the LEM summing up to a total of 100% for XX, XY, LL and RL in (001) and zz, YZ, LL and RL in (100) orientation.

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Figure 4.9: Raman spectra of TaAs in (001) and (100) orientation with different polarization settings are shown in the left and right panel, respectively. The LEMs are fitted with a Gaussian curve.

Discussion

Fig. 4.9 shows the polarization dependence of the LEM in two different orien- tâtions of TaAs. Interestingly, the LEM appears in all polarizations and on both planes. The highest integrated scattering intensity is recorded in RL with « 40% followed by XX and zz with « 30% and « 20%, respectively. XY and YZ yield the least scattering intensity with « 13%. On the contrary, the LEM in Bi2Se3 has a different polarization dependence compared to TaAs. The polarization depen­dence of Bi2Se3 is depicted in Fig. 4.10 and has been recorded by Dr. Vladimir Gnezdilov prior to this investigation.

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Figure 4.10: Exitation energy and polarization dependent Raman spectra of Bi2Se3[2].

The LEM in Bi2Se3 appears in RL but not in LL, XX and YX. In TaAs the LEM is present in RL LL, XX and XY. This behavior is rather peculiar and can not be explained by the icy condensation on the surface. This holds true provided that the measurements for the polarization dependent measurement on Bi2Se3 were realized within a time period of a few hours because of the time dependent development of the LEM. Consequently, the different polarization behavior in­dicates that a surface state could be involved.

On the other hand, topological surface state effects on TaAs are calculated to differ noticeably for surfaces in (001) and (100) orientation[33]. Fig. 4.11

illustrates the electronic surface states in (001) and (100) orientation on the left and their corresponding Fermi arcs on the right.

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Figure 4.11: Calculated electronic surface states in TaAs in (001) and (100) orien­tation shown in (a) and (c), receptively. Corresponding Fermi arcs in (001) and (100) orientation illustrated in (b) and (d), respectively[33].

The scattering behavior of the FEM would be expected to differ if generated from the topological surface state. The scattering data of TaAs in (100) and (001) orientation, presented in Fig. 4.9, illustrate that the scattering intensity of the FEM does not differ noticeably. This suggests that the FEM is not generated by a topological surface state of the material.

The polarization and orientation dependent measurements on topological materials show indications for both, a topological surface state effect and a non-topological surface state effect.

4.2.3 Excitation Energy Dependence

The laser excitation energy dependence of the LEM and phonons has been recorded for the materials TaAs, TaAs2 and ZrSiS. The applied excitation energies range between « 1.9 - 2.6 eV. Each spectrum is accompanied with the excitation wavelength. ZrSiS has been recorded by Savut jan Sidik. The data of TaAs2 originate from my bachelor thesis and TaAs was measured by myself.

Fig. 4.12 illustrates excitation energy dependent spectra of TaAs in XX and zz polarization. For both measurements, the scattering of the LEM behaves similarly for the applied excitation energies. The resonant excitation energy of the LEM emerges at « 2.4 eV (Aexc = 514.5 nm). The phonon at 255 cm-[1]has a resonant excitation energy at « 2.2 eV (Aexc = 568.2 nm). The integrated intensity of the phonon and LEM is depicted on the right of Fig. 4.13. For better visualization of the excitation dependent phonon spectrum, an enlarged view is shown on the left of Fig. 4.13.

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Figure 4.12: Raman spectra for different excitation energies on Ta As in XX and zz polarization. The samples were cooled with the Cryomech PT-405 cryostat.

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Figure 4.13: (left) Excitation energy dependent Raman spectra of the phonon at 255 cm-[1]in TaAs cooled inside the Cryomech PT-405 cryostat, (right) Nor­malized integrated intensity of the ТЕМ and phonon as a function of excitation energy.

Raman data of Ta As in RL polarization is illustrated in Fig. 4.14 (left panel). Analog to the data in zz polarization (see Fig. 4.13), the phonon at 255 cm-[1] has a resonant excitation energy at » 2.2 eV and a resonant energy at « 2.5 eV for Fig. 4.15 illustrates the excitation energy dependence of the LEM and the phonon at 171 cm-[1]in TaAs2. At an excitation wavelength of Aexc = 532.1 nm, the phonon at 171 cm-[1]has the highest scattering response compared to the other phonons. Both, the phonon at 171 cm-[1]and the LEM have a similar excitation energy dependence. The highest response occurs with an excitation wavelength between Aexc = 488.0 nm and 514.5 nm shown in the top right panel. The phonon at 171 cm-[1]is shown in the boom right panel.

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Figure 4.15: (left) Excitation energy dependent Raman spectra of TaAs2 cooled in the Cryomech PT-405 cryostat, (top right) Normalized integrated intensity of the LEM and phonon at 171 cm-[1], (bottom right) Raman spectra of the phonon at 171 cm-[1].

Raman data of ZrSiS are demonstrated in the left panel of Fig. 4.16 with the excitation energy dependence of the LEM and the phonon. An enlarged view of the phonon at 314 cm-[1]is depicted in the bottom right panel. The resonant excitation of the phonon and LEM occurs at wavelength of Aexc = 568.2 nm and Aexc = 514.5 nm, respectively.

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Figure 4.16: (left) Excitation energy dependent Raman spectra of ZrSiS cooled inside the Cryomech PT-405 cryostat, (bottom right) Raman spectra of the phonon at 314 cm-[1], (top right) Normalized integrated intensity of the LEM and phonon the at 314 cm“[1].

Discussion

A summarized analysis of the excitation energy dependent Raman spectra is depicted in Fig. 4.17. It illustrates the integrated intensities of the LEM and phonons for the spectra shown in Fig. 4.12, Fig. 4.14 (left panel), Fig. 4.15 (left panel) and Fig. 4.16 (left panel).

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Figure 4.17: Normalized integrated scattering intensity of the LEM (blue data points) and the most intense phonon for the corresponding compounds at Xexc = 532.1 nm (red data points).

The resonant excitation energy of the phonons varies from 2.2 eV to 2.5 eV. These differences are often observed in phonons and are expected for different compounds. The excitation energy with the highest Raman scattering response for the LEM is similar in all compounds with 2.48 ± 0.08 eV.

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Figure 4.18: Band structures for three temperatures. The crossings represent the WP in TaAs. The blue shades indicate the Fermi-Dirac distribution and the red arrows illustrate the probability of electronic transition[23].

The resonant scattering process of the electronic transition around the Dirac points in TaAs is expected in meV region as seen in Fig. 4.18. The resonant energy for the ТЕМ in TaAs2/ TaAs, and ZrSiS shows a resonant energy of 2.48 ± 0.08 eV, however, for resonant scattering processes as intra-band scattering do occur in high energy excitations. Electronic transition has also been reported in IR experiments in TaAs. It is published in "Temperature-tunable Fano resonance induced by strong coupling between Weyl fermions and phonons in TaAs"[23].

4.2.4 Temperature Dependence

A temperature dependent LEM had previously been reported in Bi2Se3 by Dr. Vladimir Gnezdilov (see Fig. 4.19)[2]. Dr. Alexander Glarnazda also reported having observed this temperature dependence. Based on this, temperature dependent measurements were realized.

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Figure 4.19: Temperature dependent Raman spectra of the LEM on Bi2Se3[2]

Fig. 4.20 shows temperature dependent Raman spectra of TaAs. The spectra were taken after « 200 hours of cooling the sample in the Cryomech PT-405 at 10 K. Gradually, the temperature was increased in steps and stabilized at the indicated temperatures for at least one hour for each measurement. The analysis of the normalized integrated intensity of the LEM is displayed in the right panel of Fig. 4.20. The highest scattering intensity of the LEM occurs at 24 к then rapidly declines with increasing temperature. At 50 к the LEM has only « 25% compared to the highest integrated scattering value. At 100 к the LEM is not recorded. The scattering intensity for the phonon at 255 cm-[1]does not change significantly for the different temperatures. At 10 K, the Raman spectrum is fitted with a Gaussian curve.

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Figure 4.20: (left) Temperature dependent Raman spectra of TaAs with the LEM. The sample was cooled inside the Cryomech PT-405 cryostat, (right) Normalized integrated scattering intensity of the LEM as a function of temperature.

Discussion

The Raman data TaAs and Bi2Se3 show that the LEM rapidly declines above approximately 25 K. In Bi2Se3 the LEM disappears above 40 к and in TaAs it dis­appears between 50 к and 100 K. This is shown in Fig. 4.19 and 4.20, respectively. A sudden decline of the LEM could indicate an ordering process, however, no literature for this class of material is known to the knowledge of the author. A possible explanation of this behavior might be the coexistence between the LEM and the icy condensate. With the developing icy condensate on the sur­face where the LEM effect is registered, the LEM simultaneously evolves. At a temperature high enough for the icy condensate to evaporate from the surface of the sample, the LEM also disappears. The disappearance of the LEM and the icy condensate occurs somewhere between 50 к an 100 K. Consequently, the origin of the icy condensation deserves further attention.

The origin of this condensation might be explained by the following. When the sample is installed into the Cryomech PT-405 cryostat, the sample chamber is dismantled. Prior to cooling, the a vacuum pump evacuated air from the sample chamber until a pressure of circa IO-[5]mbar is reached. During the cool­ing process the vacuum pump is continuously pumping air from the sample chamber. A leakage of the sealing possibly permits air to get inside the sample chamber which could cause the icy condensate. The condensate appears only on certain surfaces at temperatures below « 50 K. The main component of air is nitrogen N2 with 78% followed by oxygen 02 with 21%[34]. Fig. 4.21 illustrates the p-T phase diagram of N2 and 02. The phase transition between the solid and the liquid state is indicated with the red circles. In vacuum, these phase transitions occur at approximately 63 к and 54 к for N2 and 02, respectively

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Figure 4.21:ץ-Tphase diagram of N2 (left) and of 02 (right)[35]. The red circles indicate the phase transition between the liquid and solid phase in vacuum.

It is noteworthy that the solid-liquid transition temperature for both, N2 and 02, lies between 50 к and 100 K. Supposing that the LEM is generated by the frozen state of N2 and 02, it is beneficial to review Raman spectra of these elements in their solid state. These are provided in Fig. 4.22 and 4.23.

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Figure 4.22: (left) Raman spectrum of solid a-O2 in the low-energy region at 2.0 GPa[37]. (right) Raman shift frequency of the magnón and librons of a-oxygenas as function of pressure taken from various Raman experiments: squares at 6 к and 18 K, circles at 10 K, gray diamonds at 1.8 к and star at 16 к[36].

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Figure 4.23: Raman spectra of a-N2. The sample has a molar volume of 26.82 cm[3]/mol and was measured at 8 к[38].

Both, 02 and N2, host several modes in the low energy region of the Raman spectrum. Fig. 4.22 presents the Raman spectrum of a-O2 with a pressure at 2.0 GPa. It shows two distinct modes, Bg and Ag. These are librational modes or librons. Unlike classical phonons, librons are reciprocating motions where the molecule with an almost fixed orientation repeatedly rotates back and forth. When pressure is withdrawn from the sample, these modes shift to a lower Raman shift frequency as shown on the left of Fig. 4.22. In vacuum, the Raman shift of the Bg and A, mode are approximately 42 cm-[1]and 80 cm-[1], respectively.

A close analysis of the shape of the FEM reveals that the broad scattering signal conceals at least two peaks. Fig. 4.25, compares three different fits with the shape of the FEM retrieved from TaP. In the top panel, the spectrum is fitted with a Gaussian curve. Although the fit has a good accordance with the shape of the FEM in general, an additional scattering signal is distinguishable at « 85 cm-[1]. The middle panel shows the same spectrum with a Forentzian fit. It illustrates that this fit is not as suitable as the Gaussian fit. In the bottom panel of Fig. 4.25, the libron modes of a-02/ the weak continuum of N2 and the elastic scattering component from the laser-light are taken under consideration. The more abrasive the surface of the measured spot, the more diffuse laser-light passes into the spectrometer. This is illustrated in Fig. 4.24. As a consequence, elastic Rayleigh scattering increases.

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Figure 4.24: Scheme of reflected light on a flat vs. abrasive surface. More elastic light-scattering passes into the Raman spectrometer with diffuse light[39].

When icy condensate crystallizes on the surface over time, more diffuse light is scattered and gets into the spectrometer. In Fig. 4.25 the elastic light-scattering component is taken into account in the bottom panes and is shown with gray fit. The relationship of the scattering intensities between the Bg and Ag mode of 02 as shown in Fig. 4.22 is considered. The frequency position of the Bg and Ag modes in Fig. 4.22 are 43 cm-[1]and 85 cm-[1]. The sum of the modes and elastic

Scattering generates an excellent accordance to the general shape of the LEM. It fits better compared to the Gaussian and Lorentzian fit.

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Figure 4.25: Raman spectra of TaP cooled inside the Cryomech PT-405 cryostat, (top) LEM with a Gaussian fit. (middle) LEM with a Lorentzian fit. (bottom) LEM fitted with the possible Ag and Bg modes of solid 02, the continuum of N2 and the elastic Rayleigh light-scattering.

The fit provides evidence that the LEM is composed of scattering signals originating from components of frozen air.

4.2.5 Material Dependence

Samples that produced a LEM over time in Raman data are compared with pre­vious data from compounds where the LEM also appeared. These compounds are Cuo.7Bi2Se3 and Bi2Se3 and have been measured by Dr. Vladimir Gnezdilov.

All crystals were cooled with the Cryomech PT-405 cryostat at temperatures T < 10 K. Fig. 4.26 delivers the Raman data of TaAs, TaP, TaAs2/ ZrSiS, Cu0.7Bi2Se3 and Bi2Se3. For comparison, the intensity of the LEM is normalized and the spec­tra are shifted vertically for a better visualization of the data.

Abbildung in dieser Leseprobe nicht enthalten

Figure 4.26: Raman data of materials that exhibit a LEM. The samples were cooled inside the Cryomech PT-405 cryostat.

Both, the shape and Raman shift position of the LEM are similar in all shown compounds. The maximum scattering intensity occurs at 41 ± 3 cm-[1]. An over­lay of the spectra is demonstrated in Fig. 4.27. These data are normalized to the scattering intensity of the LEM. A Gaussian curve has been applied to fit the shape of the LEM.

Abbildung in dieser Leseprobe nicht enthalten

Figure 4.27: Raman data from different materials as indicated in the legend, showing the LEM normalized to its intensity. The LEM is fitted with a Gaussian fit.

Abbildung in dieser leseprobe nicht enthalten

Fig. 4.28 compares Raman spectra of three materials simultaneously measured in the Cryomech PT-405 cryostat. The material, polarization and time at the indicated temperature is illustrated in the graph. TaAs shows a time dependent LEM. CaF2 and Si do not deliver a time dependent spectrum.

Abbildung in dieser leseprobe nicht enthalten

Figure 4.28: Time dependent Raman spectra of TaAs (left), CaF2 (middle), and Si (left). The samples were cooled inside the Cryomech PT-405 cryostat.

Discussion

The main purpose of the material dependent investigation has been to examine whether the material influences the LEM. Fig. 4.26 and 4.27 deliver a striking similarity of the shape and Raman shift position of the LEM. An intrinsic sur­face effect is therefore rather improbable to produce the LEM. If the effect was intrinsic, the LEM would be expected at different Raman shift position and/or have different shapes for different crystals.

The choice of material determines if the LEM appears or not. TaAs, TaP, TaAs2/ ZrSiS, BiTel, Cuo.7Bi2Se3 and Bi2Se3 deliver a LEM, however, Si and CaF2 do not. No LEM appeared from materials where the icy condensation was ab­sent. This reinforces that there might be relation between the condensate and the LEM. As the icy condensate only crystallizes on certain material, a material specific property probably provokes this condensation. The first thought might be that this is due to the thermal conductivity of the samples, because they are attached on the coldest area inside the Cryomech PT-405 cryostat. However, considering the Stefan-Boltzmann radiation law

p = A - о · (T* - T2[4])

with the area of the sample holder: A sample holder = 2x2 cm,

temperature of the sample holder: T2 = 9 K,

and the temperature inside the sample chamber: Г! = 11 K,

the thermal exchange power of 1.8 X IO-[4]mW, is negligible for temperatures in this low region. With the an estimated sample size of A sample = 2x5 mm, the thermal exchange power only yields 4.6 X IO-[6]mW.

The texture of the material might give a possible explication. The icy conden­sate only develops on samples with a mirror-like, metallic surface (see examples in Fig. 4.1). In contrast, materials with a transparent or dull surface, for example CaF2, this type of condensate has not been observed.

Chapter 5 Summary

The investigated topological materials, mainly Weyl semi-metals and topolog­ical insulators, show interesting electronic properties related to the linear dis­persing Dirac bulk or surface states. In the following thesis, the origin of a previously observed maximum in the low energy Raman shift region has been investigated. Despite several proposals for a possible intrinsic electronic scat­tering mechanism, an intrinsic origin of this effect could not be confirmed in the present thesis. For the investigations during this thesis, different experimental parameters have been applied to differentiate and consolidated these findings.

One of the most significant indications is that the effect depends on the cryo­stat in which the sample is cooled. The LEM only appears when the sample is cooled inside the Cryomech PT-405 cryostat, but not in the other two KONTI- cryostats. In addition, the same macro-Raman setup was used in combination of two different cryostats, the Cryomech PT-405 cryostat and the KONTI-IT- cryostat type Spektro 4 to confirm that the effect is not influenced by the Raman setup. The effect should not depend on the cryostat.

Contradicting polarization dependent Raman data between Bi2Se3 and TaAs are rather peculiar. The LEM in Bi2Se3 appears in RL but not in LL, XX and YX whereas in TaAs the LEM appears in all of these polarizations. This behavior can not be easily explained by a condensate. Consequently, this suggests that a topological surface state could be involved.

Topological surface state effects on TaAs are calculated to differ significantly between the (001) and (100) surface[33]. The scattering behavior of the LEM would be expected to differ if it originated from the topological surface state, according to the orientation. The Raman data of TaAs in (100) and (001) orien-

tation (see Fig. 4.9) show that the scattering intensity of the LEM does not differ noticeably. This suggests that the LEM is not generated by a topological surface state.

Time dependent ARPES measurements of Ta As at 100 к have shown a change in the band structure over a period of two hours[32]. In our measurements the required time scale of the LEM requires 140 hours to fully develop. This time scale is rather extensive for this type of band structure development.

The temperature dependence of the LEM suggests that the effect might be of non-intrinsic nature, because the LEM suddenly declines above « 25 K. This would usually point to an ordering process. For topological materials, however, literature on ordering process for this class of materials does not exist to the knowledge of the author. The possible origin of the temperature dependent spectra might originate from the condensation of air on the sample, that possi­bly enters the cryostat though some leakage. In vacuum, nitrogen and oxygen condensate at approximately 63 к and 54 к for N2 and 02, respectively, which is in accordance of the disappearance of the LEM at temperatures above 50 K.

Raman spectra from six different materials that produce the LEM have been compared. All spectra show a remarkable similarity of the shape and Raman shift position of the LEM. For a surface effect, distinct Raman shifts position would be expected for different materials.

The icy condensate has only been observed on certain materials inside the Cryomech PT-405 cryostat and only at low temperatures operation. It has not been observed on samples with a dull or transparent, but on mirror-like, metallic surfaces. The icy condensate becomes visible after a few days. This condensation is not visible with the bare eye. A magnifying glass has to be used to enable the observation of the icy condensation.

The fit of the LEM as shown in Fig. 4.25 proposes that the LEM might not be due to a topological surface state. Even though the Gaussian curve is in good accordance with the shape of the LEM, an additional scattering signal at approximately 85 cm-[1]is noticeable. Considering literature Raman data oxygen and nitrogen in their solid state at vacuum together with the elastic Rayleigh scattering component, the fit has a good accordance with the shape of the LEM.

In conclusion, the experiments showed interesting behavior of the Low en­ergy Maximum. Topological surface state effect, however, could not be con­firmed in these experiments. There is indication that there is a relationship between a possible condensation of air inside the Cryomech PT-405 cryostat.

The appendix shows additional Raman data recorded during the master thesis. It includes data of symmetry analysis on TaAs and TaP, RE123 - high- temperature superconducting cuprates, a-Li2Ir03 - iridate with Kitaev honey­comb model, temperature dependent frequency shifts of the phonon and the antiferromagnetic comounds Cu2F2Se03 and C0Bi2O2F4.

Chapter 6 Appendix

6.1 Symmetry Analysis

Each crystal belongs to a space group with corresponding Raman tensors. These tensors have information about the vibration modes and the orientation of the crystal. The symmetry can experimentally be determined with following pa­rameters:

- polarization of incident laser light and scattered light
- surface (orientation) of the crystal
- rotation angle of the crystal relative to the polarized light

6.1.1 TaAs and TaP

TaAs and TaP have 4 atoms in their unit cell and belong to the space group /4] md (group no. 109). The corresponding Raman tensors Ri are[40]:

Abbildung in dieser leseprobe nicht enthalten

The atoms of Ta, As and p have the Wyckoff position 4a and each has the Raman active modes IA! + IB! + 2E. The irreducible representation decomposes into acoustical and optical modes

Г Raman = A! + E + A! + 2 B! + 3 E

acoustical optical

The optical modes are Raman (R) active and the acoustical modes are only infrared (I) active.

Figure 6.1: Atomic displacements for the optical phonon modes on the example of TaAs. The red number indicate the experimentally determined mode and the black number the theoretically calculated mode[41].

The Та atom is heavier than As. Hence, Та has less Raman shift than As.

Abbildung in dieser Leseprobe nicht enthalten

Figure 6.4: Raman spectra of TaP in XX and YX polarization at room temperature (top panel) and after 144 hours at 9 к (bottom panel) measured by Dr. Vladimir Gnezdilov inside the Cryomech PT-405 cryostat.

6.2 Additional Raman Measurements

6.2.1 Neon Lamp

For calibration purposes the emission spectrum of the Neon lamp has been recorded. An extract of the spectrum is shown in Fig. 6.5. Its emission frequency can be determined by calculating the absolute value of the laser line and adding the frequency of the Raman shift.

Abbildung in dieser Leseprobe nicht enthalten

Figure 6.5: Emission spectrum of a Neon lamp with literature values provided as the square data points (top panel).

6.2.2 RE123־High-Temperature Superconducting Cuprates

Despite of their high critical temperature, high-temperature superconductors (HTSC) are unconventional with respect to the role of electronic correlations dominated by Си 3d and oxygen p states. These states are also the basis for exchange coupling in the insulating, antiferromagnetic analogous. Therefore, the study of two-magnon Raman scattering plays an important role for a better understanding of the interplay between the structure and electronic properties of HTSC. With Raman experiments, the exchange coupling constant and its de­pendence on doping can be evaluated.

The here investigated samples of the composition (CaLa)(BaRE)2Cu30y, with the rare earth elements RE = Y, Nd, Dy, Gd, Sm, (also denoted as RE123) were prepared and investigated together with Amit Keren (Technion, Israel), Wayne Crump, PhD Ben Mallet and Prof. Jeff Tallon (Wellington, New Zealand).

Raman data of HTSC cuprates are characterized by their two-magnon peaks as indicated with the Lorentzian fit in Fig. 6.6, Fig. 6.7, Fig. 6.8, Fig. 6.9 and Fig. 6.10. The spectra show the RE elements together with the thermo voltage. The samples were cooled inside the KONTI-cryostat-Mikro.

Abbildung in dieser Leseprobe nicht enthalten

Figure 6.6: Raman Spectra of high-temperature superconducting cuprates with the characteristic two-magnon scattering indicated with the Lorentzian fit.

Abbildung in dieser Leseprobe nicht enthalten

6.2.3 ct־Li2Ir03 Iridate with Kitaev Honeycomb Model

Iridium oxides that follow the Kitaev model are interesting realizations of spin liquids and are presently discussed with respect to fractionalization of electronic degrees of freedom. rt-LblrCT, is a two dimensional honeycomb iridiate with possible magnetic exchange interaction that contain Kitaev interaction. The experimental investigation of magnetic Raman scattering is currently of great interest.

Raman data of rt-LblrCT, are shown in Fig. 6.11 with different excitation energies. The sample was cooled inside the KONTI-IT-cryostat type Spektro 4.

Raman shift (cm[1])

Figure 6.11: Excitation energy dependent Raman spectra of the a-LblrCh. The continua are fitted with Gaussian curves.

6.2.4 TaAs - Temperature Dependent Raman Shift of the Phonon

Fig. 6.12 presents the temperature dependent Raman data of TaAs in (100) orientation and zz polarization. The laser excitation energy applied was A = 532.1 nm. The data were taken while cooling down in steps to the desired temperature. The sample was cooled inside the KONTI-IT-cryostat type Spektro 4.

Abbildung in dieser Leseprobe nicht enthalten

Figure 6.12: Temperature dependent Raman spectra of TaAs on the (100) orien­tation.

The energy shift of the vibration mode is due to the anharmonicity, when an optical phonon decays into an acoustic one.

6.2.5 Antiferromagnetic Compounds Cu2F2Se03 and C0Bİ2O2F4

Compounds of the composition Cu2F2Se03 and C0Bİ9O9F4 have been inves­tigated together with Eleni Mitoiidi-Vagonrdi and Prof. Mats Johnsson, Univ. Stockholm, Sweden. These systems contain lone pair elements and transition metal ions leading to an interesting interplay of structure and magnetism. As a support of the PhD thesis of Eleni Mitoiidi-Vagonrdi detailed studies of the temperature dependence of the optical phonons were performed to search for evidence for magnetic or structural instabilities.

Abbildung in dieser Leseprobe nicht enthalten

Figure 6.13: Photo of a Cu2F9Se03 crystal placed on the sample holder with a hole to avoid additional scattering signals. The width of the sample is « 60 pm (about the thickness of a human hair).

Abbildung in dieser Leseprobe nicht enthalten

Abbildung in dieser Leseprobe nicht enthalten

Figure 6.15: Raman Spectra of Cu2F2Se03 with different temperature with 24 identified modes. The sample was cooled inside the KONTI-cryostat-Mikro.

Abbildung in dieser Leseprobe nicht enthalten

Figure 6.17: (top) The sudden disappearance of the phonon mode at 160 cm-[1]indicates a phase transition. This mode stiffens below a critical temperature which lies somewhere between 6 к and 50 к and is in good accordance with the magnetic susceptibility measurement that indicate a phase transition from the paramagnetic to the antiferromagnetic phase at about 50 K. (bottom left) Phonon softening, (bottom right) Relative frequency shifts of the phonons indicated in the legend. The sample was cooled inside the KONTI-IT-cryostat type Spektro Raman shift (cm[1]־)

Abbildung in dieser Leseprobe nicht enthalten

Figure 6.19: Temperature dependent Raman Spectra of C0Bİ2O2F4 indicate phase transitions at three temperatures (see arrows in bottom panel). At 243 к and 100 К structural phase transition is predicted and below 50 к the material becomes antiferromagnetic. The sample was cooled inside the KONTI-cryostat- Mikro.

Abbildung in dieser leseprobe nicht enthalten

Figure 6.20: Raman spectra of the CoBi2O2F4 with four modes around 162 cm−1 splitting at low temperature. The sample was cooled inside the KONTI-ITcryostat type Spektro 4.

List of Figures

1 Extracts from publications regarding the LEM effect[1],[2] 5

2 Auszug von Publikationen über den LEM-Effekt[1],[2] 7

1.1 Sir C. V. Raman in his laboratory with one of his inelastic light­scattering setups[4] 12

1.2 (a) Emission spectrum of a mercury arc. (b) Spectra of liquid carbon tetrachloride excited by the mercury arc radiation, (c) Scattering intensity as a function of frequency[3] 13

1.3 (left) Scheme of the energy levels in the Raman scattering process with the initial state i, an intermediate/excited state z and the final state f. (right) Conservation of momentum in the Raman scattering process[5] 15

1.4 Different alignments of molecules with the atoms A and B. It shows the displacement of the atoms and illustrates when the mode is Raman and/or infrared active[6] 17

1.5 Different vibration modes for the shown molecule with an illus­tration when the mode is Raman and/or infrared active[6] 18

1.6 Polarization of incident and scattered light on the example of a CuO-plane[7] 20

1.7 (top) Photo of the macro-Raman setup, (bottom) Scheme of the above photo with a description of its main components[10]. ... 22

2.1 Scheme of a KONTI-IT-cryostat[11] 26

2.2 Sample compartment of KONTI-IT-cryostat type Spektro 4. The sintered diffusor optimizes the cooling efficiency (gray area at the bottom). The golden-colored round plate inside the cryostat is

the sample holder 27

2.3 Photo of the setup with the KONTI-IT-cryostat type Spektro 4. (1) He-transfer line. (2) Cryostat. (3) He-vessel. (4) & (5) Vacuum pumps. (6) Heater and temperature control. (7) LHe-level monitor. 28

2.4 (left) Photo from the top part of the KONTI-IT-cryostat type Spek­

tro 4 with two connections to the vacuum system, (right) Vacuum system for the insulating vacuum 29

2.5 (left) Top part of the cryostat with the connection to the He-tank

(lilac arrow), (right) Vacuum system for the Не-tank and the sample chamber 30

2.6 (left) The interior of the KONTI-IT-cryostat type Spektro 4 with the layers: N2-tank in yellow, the vacuum chambers in light-green and the Не-tank in pastel green[11]. (right) Photo of the cryostat.

Paper tissues at the top of the cryostat to absorb condensed water

and thereby prevent refreezing during refill of LN2 32

2.7 Temperature controller TIC 304-MA used for monitoring and reg­ulating the temperature inside the sample compartment 33

2.8 A He-level monitor (AMI Model 135 Liquid Helium-Level Mon­

itor) registers the He-level in the Не-tank. The number on the display provides the percentage of the LHe-level inside the He- tank 34

2.9 Scheme of the KONTI-cryostat-Mikro with its components[12]. . 35

2.10 Overview of the KONTI-cryostat-Mikro setup. (1) Vacuum pump for the sample chamber. (2) He exhaust pump. (3) Movable X/Y table. (4) Cryostat. (5) Microscope. (6) Connection to the temperature regulation/monitoring. (7) Connection to the He-

3.3 (left) Crystal structure of Bi2Se3 with three primitive lattice vectors t13׳2׳. One quintuple layer is indicated by the red square, (a) ARPES measurements of the surface band dispersion of electronic states with a spin-polarized Dirac cone, (b) Chiral left-handed spin textures on the Fermi surface, (c) Scheme of the surface and bulk band topology, (d) A spin-polarized Dirac fermion on the surface of Bi2Se3[16],[18] 42

3.4 (left) 3D DSM hosts two sets of Dirac points with doubly degener­ate bands, (right) Electronic band dispersions of a WSM with one pair of WP. The arrows pointing inward and outward around the cone indicate magnetic monopoles that result in the Berry flux[20]. 43

3.5 (a, b) Band structure of TaAs[22]. (c) Probability of electronic states at the vicinity of the WP points in TaAs shaded in blue[23].

(d) WP of TaAs and TaP[24] . 44

3.6 (left) Crystal structure of ZrSiS. (right) ARPES data of ZrSiS show­ing the linear band dispersion. The photo energy applied was

50 eV at 20 K. . . . . 45

3.7 TaAs: (a) Crystal structure of the unit cell, (b) First Brillouin zone

List of Tables

1.1 Polarization vectors for different polarized light. A scheme of the

orientation of these vectors are depicted in Fig. 1.6 19

2.1 Advantages and disadvantages of the KONTI-IT Spektro 4, KONTI-

cryostat-Mikro and Cryomech PT-405 cryostat 25

3.1 Lattice parameters of TaAs and TaP[24],[31] 46

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