We are living in an era of digital electronics. The number of robots have already exceeded the human population of the entire earth. An article in the Guardian newspaper dated 30th March 2018 suggests that 10 million UK workers will be jobless within 15 years as they will be replaced by robots. These astonishing facts shed light on the importance of knowledge and how important it is to use it wisely for our benefit without ultimately destroying us. Knowledge in all forms is accessible without going to a library or buying a newspaper. Furthermore to access information, we often use sleek devices such as smart phones, using highly developed multimedia platforms which consume large amounts of power. In 2016, IBM found that humans create 2.5 quintillion bytes of data daily. Since high computing usage is related to large power consumption, the basic building block of electronics i.e. the transistor is required to be more power efficient. This is now possible through spintronics, where the spin of an electron is exploited instead of the charge. A new class of exotic materials called topological insulators are predicted to exhibit efficient spintronic applications. These materials can conduct spin polarised current on their surface while remaining completely insulting from the inside. Moreover, doping topological insulators with magnetic impurities unlocks new avenues for spin memory devices in the form of a single spin polarized dissipationless conduction channel. In topological insulators, there is always a contribution from the inside (bulk) in addition to surface conduction, thereby yielding charge transport rather than spin transport. On this basis, the aim of my PhD was to explore techniques to grow, characterize, fabricate and measure devices on topological Dirac materials, with the hope to experimentally distinguish the bulk from the surface states and also exploit their exotic properties arising from opening of the bulk band gap by intentional magnetic doping. Samples consisted of thin films of Bi2Se3, Sb2Te3, Cr doped Sb2Te3, bilayers of Dy doped Bi2Te3/Cr doped Sb2Te3 and Cd3As2 nanowires. It was found that a seed layer of an undoped topological insulator was a crucial first step to ensure high quality growth by molecular beam epitaxy, followed by the desired stoichiometry. By physically doping Sb2Te3 with Cr, a successful control of the magnetic and electrical properties such as coercivity, anomalous Hall resistance RA xy, Curie temperature Tc, carrier density and mobility were achieved. A substitutional Cr doping ranging from 7.5% to 38% was attained revealing a Tc reaching up to 186 K. Gated electrical measurements displayed a change in RA xy and carrier density by ~ 50% on applicating of just -3 V gate bias in a sample with 29% doping. A comparison between electrical transport, Magneto-optical Kerr effect and terahertz time domain spectroscopy measurements revealed that the mechanism of magnetization was RKKY mediated. Furthermore, the bilayer structure displays a clear exchange bias coupling arising from the proximity of the antiferromagnetic Dy doped Bi2Te3 layer with the ferromagnetic Cr doped Sb2Te3 layer. Electrical transport measurements on Bi2Se3 Hall bars fabricated using Ar+ milling and wet chemical etching were compared. The results showed a more bulk type response in the chemical etched sample even though Ar+ milling was responsible for creating more disorder in the system leading to a higher carrier density and lower mobility. A thickness dependent study on Sb2Te3 thin films revealed a single conducting channel associated with a coupled surface and bulk state for a 12 nm sample, compared to, two conducting channels associated with the top and bottom surfaces for the 25 nm sample. Electrical transport on Dirac semimetal Cd3As2 nanowires reveal an ultra-high mobility of 56884 cm2V-1s-1 at 1.8 K from analysis of Shubnikov-de Haas oscillations. By studying various Dirac materials, new avenues for practical device applications can be explored.

One of the major challenges for the semiconductor industry is to continue with the miniaturization of the device features, increasing the integration densities with higher operation frequency. Silicon the material of choice so far, has been arriving at its physical limits which has led the condensed matter researchers to look for alternative new material which can set the foundation for the next generation computing paradigms or lead to applications in spintronics. There has been a rising interest in so-called Dirac materials, characterized by a linear dispersion relation, giving rise to exotic physical phenomena such as high carrier velocities ~ 106 m/s and dissipationless charge transport. In this thesis, we have studied two classes of Dirac materials - graphene and topological insulators (TIs) namely, bismuth selenide (Bi2Se3) and antimony telluride (Sb2Te3). Specifically, we investigate the optical behavior of Dirac materials using terahertz time domain spectroscopy (THz-TDS) contact-free optical technique, used to probe the low-energy excitations in strongly correlated electron gases. Chapter 1 provides a broad introduction to the field of topological insulators and graphene the various optical and electronic methods, which have been employed to explore their response. In particular the focus in on detecting and isolating the response from the topological surface state (TSS) in TIs, which are “robust”, as it is protected against backscattering by spin− momentum locking and time reversal symmetry. Various literature reports describing the current understanding of the TI field are then discussed. This sets the context for understanding the approach undertaken in the rest of the thesis, towards investigating these materials. In Chapter 2 we discuss the intrinsic plasmonic response in chemical vapour deposited (CVD) graphene and its relation to the domain size of graphene. A novel ion gel based top gate is implemented with the possibility of tuning the plasmonic resonances by ~ 70 GHz. We further employ THz-TDS to map the conductivity of graphene film on different substrates such as germanium and sapphire. In chapter 3, we investigate Bi2Se3, a representative TI using THz spectroscopy and magnetotransport measurements. The temperature-dependent optical behavior of a 23-quintuple-thick film of Bi2Se3, is used to deconvolve the surface state response from the bulk resulting in an optical mobility exceeding 2000 cm^2/V·s at 4 K, indicative of a surface-dominated response. Further, a scattering lifetime of ∼0.18 ps and a carrier density of 6 × 10^12 cm^−2 at 4 K is obtained using the THz measurements. The electrical transport measurements reveal weak antilocalization behavior in the Bi2Se3 sample, consistent with the presence of a topological surface state. Chapter 4, discusses the phase transition in a rather less considered TI, Sb2Te3, using THz-TDS. We track through a series of topological phase transitions from 3D-TI to 2D hybrid topological insulator and then a 2D trivial insulator, as function of Sb2Te3 film thickness. Reducing the film thickness further resulted in a reduced mobility suggesting that the formation of a spin-conserving scattering channel characteristic of hybridized topological insulator phase. Finally, the Chapter 5, concludes with a summary of the thesis and presents future opportunities for further research arising from this work.

The three key areas of this thesis are crystal synthesis strategies, growth mechanisms, and new types of quantum materials nanowires. The highlights are introduction of a new catalyst (TiO2) for nanowire growth and application to Bi2Se3, Bi2Te3, SnO2, and Ge nanowires; demonstration of step-flow growth, a new growth mechanism, for Bi2Te3 sub-micron belts; and the characterisation of the first quasi-one dimensional topological insulator (orthorhombic Sb-doped Bi2Se3) and topological Dirac semimetal nanowires (Cd3As2). Research into new materials has been one of the driving forces that have contributed to the progress of civilisation from the Bronze Age four thousand years ago to the age of the semiconductor in the 20^th century. At the turn to the 21^st century novel materials, so-called quantum materials, started to emerge. The fundamental theories for the description of their properties were established at the beginning of the 20^th century but expanded significantly during the last three decades based, for example, on a new interpretation of electronic states by topological invariants. Hence, topological insulator (TI) materials such as mercury-telluride are one manifestation of a quantum material. In theory, TIs are characterised by an insulating interior and a surface with spin-momentum locked conduction. In real crystals, however, the bulk can be conducting due to crystal imperfections. Nanowires suppress this bulk contribution inherently by their high surface-to-volume ratio. Additionally, trace impurity elements can be inserted into the crystal to decrease the conductance further. These optimised TI nanowires could provide building blocks for future electronic nanodevices such as transistors and sensors. Initial synthesis efforts using vapour transport techniques and electronic transport studies showed that TI nanowires hold the promise of reduced bulk contribution. This thesis expands the current knowledge on synthesis strategies, crystal growth mechanisms, and new types of quantum materials nanowires. Traditionally, gold catalyst nanoparticles were used to grow TI nanowires. We demonstrate that they are suitable to produce large amounts of nanowires but have undesired side-effects. If a metaloxide catalyst nanoparticle is used instead, quality and even quantity are significantly improved. This synthesis strategy was used to produce a new TI which is built from chains of atoms and not from atomic layers as in case of previously known TIs. The growth of large nanowires with a layered crystal structure leads to step-flowgrowth, an intriguing phenomenon in the growth mechanism: New layers grow on top of previous layers with a single growth frontmoving fromthe root to the tip. These wires are ideal for further electronic characterisation that requires large samples. The nanowire growth of tin-oxide will also be discussed, a side project that arose from my growth studies, which is useful for sensor applications. Under certain conditions it forms tree-like structures in a single synthesis step. All of the aforementioned growth studies are carried out at atmospheric pressure. A separate growth study is carried out in ultra-high vacuum to assess the transferability of the growth process towards the cleanliness requirements of the semiconductor industry. If two quantum materials are joined together, exotic physics may emerge at the interface. One of the goals of TI research is the experimental observation of Majorana fermions, exotic particles which are their ownantiparticles with potential applications in quantum computing that may appear in superconductor/TI hybrid structures. We have synthesised such structures and initial characterisation suggests that the resistivity increases when they are cooled below the critical temperature of the superconductor. Beyond TIs, a new type of quantum material, called a topological Dirac semimetal, opens new realms of exotic physics to be discovered. Nanowires are grownfroma material which has recently been discovered to be a topological Dirac semimetal. Their growth mechanism is characterised and an extremely high electron mobility at room temperature is measured. The contribution of this thesis to the field is summarised in Fig. 1. Its core is the study of the growth mechanism of quantum materials which will be vital for future development of applications and fundamental research.

Thesis advisor: Vidya Madhavan / Spin-orbit coupling (SOC) is the interaction of an electron's intrinsic angular momentum (spin) with its orbital momentum. The strength of this interaction is proportional to Z<super>4</super> where Z is the atomic number, so generally it is stronger in atoms with higher atomic number, such as bismuth (Z=83) and iridium (Z=77). In materials composed of such heavy elements, the prominent SOC can be sufficient to modify the band structure of the system and lead to distinct phase of matter. In recent years, SOC has been demonstrated to play a critical role in determining the unusual properties of a variety of compounds. SOC associated materials with exotic electronic states have also provided a fertile platform for studying emergent phenomena as well as new physics. As a consequence, the research on these interesting materials with any insight into understanding the microscopic origin of their unique properties and complex phases is of great importance. In this context, we implement scanning tunneling microscopy (STM) and spectroscopy (STS) to explore the surface states (SS) of the two major categories of SOC involved materials, Bi-based topological insulators (TI) and Ir-based transition metal oxides (TMO). As a powerful tool in surface science which has achieved great success in wide variety of material fields, STM/STS is ideal to study the local density of states of the subject material with nanometer length scales and is able to offer detailed information about the surface electronic structure. In the first part of this thesis, we report on the electronic band structures of three-dimensional TIs Bi₂Te₃ and Bi₂Se₃. Topological insulators are distinct quantum states of matter that have been intensely studied nowadays. Although they behave like ordinary insulators in showing fully gapped bulk bands, they host a topologically protected surface state consisting of two-dimensional massless Dirac fermions which exhibits metallic behavior. Indeed, this unique gapless surface state is a manifestation of the non-trivial topology of the bulk bands, which is recognized to own its existence to the strong SOC. In chapter 3, we utilize quasiparticle interference (QPI) approach to track the Dirac surface states on Bi₂Te₃ up to ~800 meV above the Dirac point. We discover a novel interference pattern at high energies, which probably originates from the impurity-induced spin-orbit scattering in this system that has not been experimentally detected to date. In chapter 4, we discuss the topological SS evolution in (Bi_1-xIn_x)₂Se₃ series, by applying Landau quantization approach to extract the band dispersions on the surface for samples with different indium content. We propose that a topological phase transition may occur in this system when x reaches around 5%, with the experimental signature indicating a possible formation of gapped Dirac cone for the surface state at this doping. In the second part of this thesis, we focus on investigating the electronic structure of the bilayer strontium iridate Sr₃Ir₂O₇. The correlated iridate compounds belong to another domain of SOC materials, where the electronic interaction is involved as well. Specifically, the unexpected Mott insulating state in 5<italic>d</italic>-TMO Sr₂IrO₄ and Sr₃Ir₂O₇ has been suggested originate from the cooperative interplay between the electronic correlations with the comparable SOC, and the latter is even considered as the driving force for the extraordinary ground state in these materials. In chapter 6, we carried out a comprehensive examination of the electronic phase transition from insulating to metallic in Sr₃Ir₂O₇ induced by chemical doping. We observe the subatomic feature close to the insulator-to-metal transition in response with doping different carriers, and provide detailed studies about the local effect of dopants at particular sites on the electronic properties of the system. Additionally, the basic experimental techniques are briefly described in chapter 1, and some background information of the subject materials are reviewed in chapter 2 and chapter 5, respectively. / Thesis (PhD) — Boston College, 2014. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

The generation of electron-hole pairs in materials has great importance. In direct bandgap semiconductor materials, the mechanism of radiative recombination of electron-hole pairs leads to the emission of photons, which is the basis of Light Emitting Diodes (LEDs). The excitation of electron-hole pairs by absorption of photons is the active process in photodiodes, solar cells, and other semiconductor photodetector devices. In optoelectronic devices such as optical switches which are based on transmission and reflection of the photons, electron-hole pairs excitation is a key for the device performance. Diodes and transistors are also great discoveries in electronics which rely on the generation and recombination of electron-hole pairs at p-n junctions. In three-dimensional topological insulators (3D TIs) materials nanostructures excitation of electron-hole pairs can be utilized for the quantum memory, quantum information and quantum teleportation. In two-dimensional (2D) layered materials like graphene, MoS2, MoSe2, WS2 and WSe2 generation and recombination of electron hole pairs is main process at p-n junctions, infrared detectors and sensors. This PhD thesis is concerned with the physics of different types of electron-hole pairs in various materials, such as wide-bandgap semiconductors, 3D topological insulators, and plasmonic excitations in metallic nanostructures. The materials of interest are wide bandgap semiconductors such as TiO2 , 3D TIs such as Pb1-xSnxTe and the 2D layered materials such as MoS2 and MoO3. We study the electronic and optical properties in bulk and nanostructures and find applications in the area of semiclassical and quantum information processing. One of the interesting applications we focus in this thesis is shift in surface plasmon resonance due to reduction in index of refraction of surrounding dielectric environment which in turns shifts the wavelength of surface plasmon resonance up to 125 nm for carrier density of 10^22/cm^3. Employing this effect, we present a model of a light controlled plasmon switching using a hybrid metal-dielectric heterostructures. In 3D TIs nanostructures, the time reversible spin partners in the valence and conduction band can be coupled by a left and a right handed circular polarization of the light. Such coupling of light with electron-hole pair polarization provides an unique opportunity to utilize 3D TIs in quantum information processing and spintronics devices. We present a model of a 3D TI quantum dot made of spherical core-bulk heterostructure. When a 3D TI QD is embedded inside a cavity, the single-photon Faraday rotation provides the possibility to implement optically mediated quantum teleportation and quantum information processing with 3D TI QDs, where the qubit is defined by either an electron-hole pair, a single electron spin, or a single hole spin in a 3D TI QD. Due to excellent transport properties in single and multiple layers of 2D layered materials, several efforts have demonstrated the possibility to engineer electronic and optoelectronic devices based on MoS2. In this thesis, we focus on theoretical and experimental study of electrical property and photoluminescence tuning, both in a single-layer of MoS2.We present theoretical analysis of experimental results from the point of view of stability of MoO3 defects in MoS2 single layer and bandstructures calculation. In experiment, the electrical property of a single layer of MoS2 can be tuned from semiconducting to insulating regime via controlled exposure to oxygen plasma. The quenching of photoluminescence of a single sheet of MoS2 has also been observed upon exposure to oxygen plasmas. We calculate the direct to indirect band gap transitions by going from MoS2 single sheet to MoO3 single sheet during the plasma exposure, which is due to the formation of MoO3 rich defect domains inside a MoS2 sheet.

Quantum information technologies offer significantly more computational power for certain tasks and secure communication lines compared to the available classical machines. In recent years there have been numerous proposals for the implementation of quantum computers in several different systems that each come with their own advantages and challenges. This dissertation primarily focuses on challenges, specifically interactions with the environment, and applications of two of such systems: Semiconductor quantum dots and topological insulators. The first part of the dissertation is devoted to the study of semiconductor quantum dots as candidates for quantum information storage and sources of single-photon emission. The spin of the electron trapped in a self-assembled quantum dot can be used as a quantum bit of information for quantum technology applications. This system possesses desirable photon emission properties, including efficiency and tunability, which make it one of the most advanced single-photon emitters. This interface is also actively explored for the generation of complex entangled photonic states with applications in quantum computing, networks, and sensing. First, an overview of the relevant developments in the field will be discussed and our recent contributions, including protocols for the control of the spin and a scheme for the generation of entangled photon states from coupled quantum dots, will be presented. We then look at the interaction between the electron and the surrounding nuclear spins and describe how its interplay with optical driving can lead to dynamic nuclear polarization. The second part of the dissertation follows a similar study in topological insulators: The role of time-reversal breaking magnetic impurities in topological materials and how spinful impurities enable backscattering mechanisms by lifting the topological protection of edge modes. I will present a model that allows for an analytical study of the effects of magnetic impurities within an experimental framework. It will be discussed how the same platform also enables a novel approach for applications of spintronics and quantum information, such as studying the entanglement entropy between the impurities and chiral modes of the system. / Doctor of Philosophy / Quantum information science has received special attention in recent years due to its promising advantages compared to classical machines. Building a functional quantum processor is an ongoing effort that has enjoyed enormous advancements over the past few years. Several different condensed matter platforms have been considered as potential candidates for this purpose. This dissertation addresses some of the major challenges in two of the candidate platforms: Quantum dots and topological insulators. We look at methods for achieving high-performance optical control of quantum dots. We further utilize quantum dots special ability to emit photons for specific quantum technology applications. We also address the nuclear spin problem in these systems which is the main source of destruction of quantum information and one of the main obstacles in building a quantum computer. This is followed by the study of a similar problem in topological insulators: Addressing the interaction with magnetic impurities of topological insulators. Included with each of these topics is a description of relevant experimental setups. As such, the studies presented in this dissertation pave the way for a better understanding of the two major obstacles of hyperfine interactions and the optical controllability of these platforms.

Recently, Bi₂Se₃ was added to a new class of materials known as topological insulators. While several studies have provided tantalizing hints towards novel physical properties, such as backscatter suppression and spin-polarized transport, several concerns remain in actual materials. In particular, high defect densities, strong surface band bending, and potential fluctuations have been observed. Here, scanning tunneling microscopy and spectroscopy are used to reveal surface effects in Bi₂Se₃ and CuxBi₂Se₃. First, a detailed examination of defects in bulk-grown samples is described. Then, I provide an analysis of molecular beam epitaxy results, done in collaboration with colleague Yuxuan Chen. Following this, I provide a detailed study of individual point defects in Cu-doped Bi₂Se₃ and examine how Cu is incorporated into the Bi₂Se₃ lattice. Finally, through spectroscopic analysis, a novel depth-sensitive measurement of the local band bending field is developed. Furthermore, for the first time, fluctuations of the Dirac point can be correlated to specific near-surface defects, namely Se vacancies. These analyses provide valuable insights into the preparation of future samples for the investigation of topological insulators. / text

Since the discovery of the long-range ferromagnetic order in two-dimensional and multi-layered van der Waals crystals, and the observation of a nontrivial topology of the magnon bulk bands in the chromium trihalides, the bosonic honeycomb lattices have drawn significant attention within the condensed matter community. In this thesis, we employ a Heisenberg model with a Dzyaloshinsky-Moriya interaction in a honeycomb ferromagnetic lattice to study the properties of bulk and edge spin-wave excitations (magnon). By the Holstein-Primakoff transformations in the linear spin-wave approximation, the spin Hamiltonian is written as the bosonic equivalent of the Haldane model for spinless fermions. We present a simple bosonic tight binding formalism which allows us to obtain analytical solutions for the energy spectrum and wavefunctions. We investigate three basic boundaries in the honeycomb lattice: zigzag, bearded and armchair, and we derive analytical expressions for the energy band structure and wavefunctions for the bulk and edge states, and with both zero and nonzero Dzyaloshinsky-Moriya interaction. We find that in a lattice with a boundary, the intrinsic on-site interactions along the boundary sites generate an effective defect and this gives rise to Tamm-like edge states. If a nontrivial gap is induced, both Tamm-like and topologically protected edge states appear in the band structure. The effective defect can be strengthened by an external on-site potential, and the dispersion relation, velocity and magnon density of the edge states all become tunable. We also investigate the bond modulation in the bosonic Haldane model, where by introducing a Kekule bond modulation and with the analysis of the gap closing conditions and the bulk band inversions, we find a rich topological phase diagram for this system yet to be discovered. We identify four topological phases, verified by a numerical calculation of the Chern number, in terms of the Kekule modulation parameter and the Dzyaloshinsky-Moriya interaction. We present the bulk-edge correspondence for the magnons in a honeycomb lattice for both armchair and zigzag boundaries. We believed that our study in this thesis will be important for possible applications of magnons in data process devices such as magnonics.

This thesis outlines the development of two new techniques that exploit very small structures, on the micro- and nano-scale, to enable innovative electrical transport measurements on a variety of materials of current interest in condensed matter physics. The first technique aims to apply the versatility of electron-beam lithography for micro-fabrication of patterned electronic circuitry to the problem of performing transport experiments on individual crystallites taken from a typical powder sample. We show that these small samples, tens of microns in size, are actually often very high quality single crystals and can be exploited for measurements of electrical transport in materials of which no larger crystals are available. By way of demonstration, we present the results of preliminary transport measurements on a crystallite of the layered oxide chalcogenide Sr₂MnO₂Cu_1.5Se₂. We report a phase transition in the resistivity at 213K which may correspond to the onset of previously reported short-range order in copper and vacancy sites in the Cu_1.5Se₂ planes. The second technique is designed to investigate the topological protection of surface transport in 3-D topological insulators. We decorate the surfaces of single-crystal samples with two different species from a well-characterised family of single-molecule magnets. The two coatings have an electrostatically identical influence on the sample surface, but differ in that one species carries a spin and the other is spinless. The spinless molecule acts as a control, to allow us to cleanly determine the influence of the magnetic component of a scattering potential on transport in the surface. With this technique we investigate proposed topological Kondo insulator SmB₆. We find that the surface state dominates low-temperature transport and demonstrate that the momentum relaxation is very sensitive to a spin degree of freedom in the scatterer, in keeping with expectations of a topological insulator.

Cette thèse porte sur l'exploration de différentes phases topologiques présentes dans des hétérostructures à base de mercure, cadmium et tellure (HgCdTe). Ces systèmes sont de parfaits cas d'études des états topologiques dans la matière condensée. En effet, leur structure de bande peut aisément être modifiée d'inversée à non-inversée par le biais de paramètres internes ou externes.Lorsqu'un système présente une structure de bande inversée, il a une topologie non triviale. Il est impossible de modifier cet ordre topologique sans fermer son gap, ce qui inévitablement entraîne l'apparition de particules sans masse dans son volume. Un système présentant une structure de bande inversée et un gap d'énergie finie dans lequel se trouve le niveau de Fermi, est appelé isolant topologique. Ce nouveau type de matériau est isolant dans son volume, mais abrite des états métalliques sans gap sur ses bords. Ces derniers ont une relation de dispersion linéaire et sont protégés des effets liés au désordre et de la rétrodiffusion par des impuretés non magnétiques. Ces états particuliers apparaissent à l'interface de matériaux présentant des ordres topologiques différents. Ainsi, un isolant topologique 2D se caractérise par des canaux 1D de conductance polarisés en spin à ses bords, alors qu'un isolant topologique 3D accueille des fermions de Dirac 2D, polarisés en spin, aux surfaces.L'existence de fermions sans masse 2D et 3D a déjà été démontrée expérimentalement. Cependant, la transition de phase topologique durant laquelle apparaissent les particules sans masse n'a que très peu été explorée. Il est possible de modifier la structure de bande de HgCdTe d'inversée à non inversée par le biais de la composition chimique, la pression, la température ou le confinement quantique. Ces paramètres permettent ainsi de sonder le système au voisinage de différentes transitions de phase topologiques. Dans ce travail, l'utilisation de la température comme paramètre d'ajustement continu du gap permet d'étudier au point de transition de phase l'apparition de fermions semi-relativistes de Dirac (2D) et de Kane (3D) ainsi que leurs propriétés.Les systèmes étudiés au cours de ces travaux de recherche sont des cristaux massifs de Hg1-xCdxTe et des puits quantiques HgTe/CdTe présentant des structures de bandes inversées et non inversées, ainsi que des couches minces de HgTe contraintes pouvant être considérées comme des isolants topologiques 3D ayant un confinement quantique résiduel. Tous ces systèmes possèdent des propriétés topologiques. L'interprétation des résultats s'appuie sur les prédictions théoriques basées sur le modèle de Kane. En annexe, une vue d'ensemble des puits quantiques composites InAs/GaSb, structures également identifiées comme isolants topologiques, est présentée, comportant les résultats préliminaires obtenus sur ces dernières.Toutes les structures ont été étudiées par magnétospectroscopie en transmission dans les domaines de fréquence terahertz et infra-rouge moyen à l'aide d'un dispositif expérimental spécifiquement conçu pour permettre des mesures sur une large plage de températures. / This thesis presents an investigation of different topological phases in mercury-cadmium-telluride (HgCdTe or MCT) based heterostructures. These solid state systems are indeed a perfect playground to study topological states, as their band structure can be easily varied from inverted to non-inverted, by changing internal or external parameters.If a system has an inverted band ordering, its electronic structure has a non-trivial topology. One cannot change its topological order without closing the band gap, which is inevitably accompanied with the appearance of massless particles in the bulk. A system, that has an inverted band structure and a finite gap in which the Fermi level is positioned, is called a topological insulator. These novel materials are insulators in the bulk, but host gapless metallic states with linear dispersion relation at boundaries, protected against disorder and backscattering on non-magnetic impurities. These states arise at the interfaces between materials characterized by a different topological order. A 2D topological insulator is thus characterized by a set of 1D spin-polarized channels of conductance at the edges, while a 3D topological insulator supports spin-polarized 2D Dirac fermions on its surfaces.The 2D and 3D massless fermions have already been demonstrated experimentally in HgCdTe-based heterostructures. However, the topological phase transitions during which the massless particles appear remain barely explored. The HgCdTe band structure can be tuned from inverted to non-inverted using chemical composition, pressure, temperature, or quantum confinement. These parameters therefore allow to probe the system in the vicinity of different topological phase transitions. In this thesis, the use of temperature as continuous band gap tuning parameter allows to study the appearance and the parameters of semi-relativistic 2D Dirac and 3D Kane fermions emerging at the points of phase transitions.The systems investigated were Hg$_{1-x}$Cd$_x$Te bulk systems and HgTe/CdTe quantum wells characterized by an inverted and regular band order, and strained HgTe films which can be considered as 3D topological insulators with a residual quantum confinement. All these systems exhibit topological properties, and the experimental results are interpreted according to theoretical predictions based on the Kane model. This thesis is complemented by an overview and the preliminary results obtained on a different compound -- a InAs/GaSb broken-gap quantum well, which was also identified as a topological insulator. The structures were studied by means of terahertz and mid-infrared magneto-transmission spectroscopy in a specifically designed experimental system, in which temperature could be tuned in a broad range.