In this thesis, I show my effort in growing atomically flat Bi₂Se₃ thin films using molecular beam epitaxy (MBE) method. Bi₂Se₃ is a kind of topological insulator, whose exotic surface states have been found in the samples that I grew. / text

三維拓樸絕緣體，其擁有表面可以導電但內部卻屬於絕緣體的特殊性質；近年來成為熱門的研究領域。拓樸保護表面態此種獨特性質使得拓樸絕緣體有潛力成為自旋電子學研究材料。在已發表的文獻中可以得知Bi2Te3系列材料已經被證實為拓樸絕緣體。我們製作了一系列的Bi1.5Sb0.5Te3-ySey材料，希望藉由硒元素的摻雜改變在狄拉克錐體附近的能帶結構以更詳加了解拓樸絕緣體表面性質以及其物理特性。他們的晶格結構為菱形六角面體；當摻雜量y=1.6時，a軸及c軸的晶格常數分別為4.25 Å以及29.80 Å；同時也發現晶格常數隨著硒元素的摻雜量提高而逐漸遞減。為了更進一步了解拓樸絕緣體物理性質，我們做了電阻率、磁阻以及霍爾效應的量測以及分析。電阻率的結果顯示，樣品在高溫時呈現絕緣體的電阻性質，但在低溫時表面態傳導電子開始主導而電阻上升趨勢轉趨於平緩。在霍爾效應中看到低溫至高溫由p-type轉n-type，並且其變化溫度和硒元素摻雜有直接關聯。高溫的n-type載子歸咎於於能隙間的Donor Level受熱後激發電子至傳導帶，最後取代原有的電洞使材料變成n-type。透過阿瑞尼士方程式，可由電阻對溫度曲線計算其活化能，同時可以了解低溫下電阻反曲及載子型態改變之間的關係。我們在磁阻量測中觀察到了弱反局域效應，並且從2 K的數據中顯示此現象和硒元素的摻雜沒有直接關聯性。 / 3D Topological insulator (TI), a type of material that insulates inside bulk and conducts on the surfaces, becomes a popular topic in recent years. The unique topologically protected surface states turn topological insulator to be a potential spintronic material. Bi2Te3 based materials have been studied and identified as topological insulators. In order to study the properties of the surface states, a series of specimens of Bi1.5Sb0.5Te3-ySey (BSTS) with y=1.1, 1.2, 1.4, and 1.6 were fabricated for tuning the band gap around Dirac cone. The lattice structure of Bi1.5Sb0.5Te3-ySey is confirmed to be rhombohedral. For the specimen y=1.4 the lattice constants a ̂ and c ̂are 4.25Å and 29.80Å respectively. The lattice constants decrease with Se substitution increase. To characterize the TI properties, the resistivity, magnetoresistance and Hall effect were studied. Resistivity showed an insulator behavior at high temperatures and surface conduction behavior at low temperatures. The dominate carriers are p-type at low temperatures and become n-type at high temperatures. According to the correlations of resistivity and Hall effect of Bi1.5Sb0.5Te3-ySey, we observed that thermal activation can be tuned by Selenium dopants. The weak anti-localization was also observed in our bulk samples. From the 2 K magnetoresistance, we observed that weak anti-localization was independent on Selenium and Tellurium concentrations in all specimens.

The study of topological superconductivity has been at the forefront of condensed matter physics for the past few years. Topological superconductors are predicted to have odd parity pairing and host so called Majorana fermions, which are not only of fundamental importance, but also proposed to be building blocks for fault-tolerant quantum computing. In this dissertation, we use point contact spectroscopy to study the pairing symmetry of candidate topological superconducting materials. We study proximity induced superconductivity in the topological insulator Bi2Se3 by a superconducting niobium tip, and propose a model to explain its features in point contact spectra. We further study the nature of the superconductivity in highly doped superconducting topological insulators, including CuxBi2Se3 and Sn1-xInxTe, using both a normal metal gold tip and a superconducting niobium tip. For CuxBi2Se3, we observe a robust zero-bias conductance peak (ZBCP) in the differential conductance spectra with the gold point contact, while with the niobium point contact we find the height of the peak exhibiting unusual non-monotonic temperature dependence. We argue that both observations cannot be explained by Andreev reflection within the standard Blonder-Tinkham-Klapwijk (BTK) model, but signify unconventional superconductivity in the material. For Sn1-xInxTe samples, we observe ZBCP in the differential conductance spectra with the gold point contact, while with the niobium point contact, the temperature dependence of ZBCP is monotonic as expected from conventional theory, leaving the nature of the superconductivity of Sn1-xInxTe still an open question.

Cette thèse a pour but de développer et d'utiliser un cadre cohérent permettant de caractériser les phases topologiques dans des milieux spatialement périodiques induites par une perturbation dépendant périodiquement du temps ("phases topologiques de Floquet" ou "isolants topologiques de Floquet"), en présence de symétries. Ces phases sont des généralisation des isolants topologiques apparues lors de l'étude d'isolants topologiques induits par la lumière ainsi que d'analogues ondulatoires des isolants topologiques (en acoustique, mécanique et optique). De nouveaux invariants topologiques caractérisant ces systèmes sont définis, en particulier en présence d'un renversement du temps fermionique. Les cas, déjà connus dans des situations particulières, des classes complexes A et AIII de Cartan-Altland-Zirnbauer sont généralisés à toutes les dimensions, et leur survivance dans les classes réelles est discutée. Les conséquences physiques potentielles dans des systèmes électroniques sont explorées par des simulations de transport résolues en temps, qui concluent à l'existence de conductances différentielles moyennes quantifiées en présence d'un état de bord topologique. / This thesis aims at developing and using a coherent framework to characterize topological states in spatially periodic media stemming from a time-periodic drive (« topological Floquet states » or « Floquet topological insulators »), when symmetries are present. Such states are a generalization of topological insulators, which appeared from the study of the control by light of topological insulators, and from the study of the wave-physics versions of topological insulators (in acoustics, mechanics and optics). New invariants characterizing such systems are defined, in particular when fermionic time-reversal is present. The cases of complex classes A and AIII in the Cartan-Altland-Zirnbauer classification, which are already known in particular cases, are generalized to any space dimension, and their survival in real classes is discussed. Potential physical consequences in electronic systems are explored by time-resolved numerical simulation of transport properties, which show evidence of quantized average differential conductances when a topological edge state is present.

Band structures of ultrathin films of heavy elements, £\-Sn and Sb, were investigated using first-principle calculations with the inclusion of spin-orbit coupling. The band structures were gradually varied as the physical parameters were adjusted. The band inversion was obtained at the high symmetry point in Brillouin zone, making a topological phase transition. In this study, the band inversion at £F point of the Brillouin zone was predicted in single bi-layer of Sb(111) and single bi-layer and two bi-layers of £\-Sn(111). The topological phase transition is from trivial insulator to topological insulator for single bi-layer of Sb(111). Finally, the topological phase transition is from trivial semi-metal to topological semi-metal for single bi-layer of £\-Sn(111), whereas as it is from topological semi-metal to trivial metal for two bi-layers of £\-Sn(111).

Since their experimental discovery in 2008, topological insulators have been catapulted to the forefront of condensed matter physics research owing to their potential to realize both exciting new technologies as well as novel electronic phases that are inaccessible in any other material class. Their exotic properties arise from a rare quantum organization of its electrons called ``topological order,'' which evades the conventional broken symmetry based-classification scheme used to categorize nearly every other state of ordered matter. Instead, topologically ordered phases are classified by topological invariants, which characterize the phase of an electron's wavefunction as it moves through momentum space. When a topologically ordered phase is interfaced with an ordinary phase, such as the vacuum, a novel metallic state appears at their shared boundary. In topological insulators, this results in the formation of a two-dimensional metallic state that spans all of its surfaces. The surface state electronic spectrum is characterized by a single linearly dispersing and helically spin-polarized Dirac cone that is robust against disorder. The helical nature of the surface Dirac cone is highly novel because the Dirac electrons carry a net magnetic moment and are capable of transporting 100% spin-polarized electrical currents, which are the long-sought electronic properties needed for many spin-based electronic applications. However, owing to the small bulk band gap and intrinsic electronic doping inherent to these materials, isolating the surface electronic response from the bulk has proven to be a major experimental obstacle. In this thesis, we demonstrate the means by which light can be used to isolate and study the surface electronic response of topological insulators using optoelectronic and nonlinear optical techniques. In chapter 1, we overview the physics of topological order and topological insulators. In chapter 2, we show how polarized light can be used to generate and control surface electrical currents that originate from the helical Dirac cone. In chapter 3, we demonstrate that the nonlinear second harmonic generation of light from a topological insulator is a sensitive surface probe and can be used to detect the breaking of space-time symmetries and monitor changes in the surface carrier density. / Physics

Topological Insulator (TI) is new classes of materials with gapless surface states and insulating bulk. The topological connection can be traced back to the discovery of Integer Quantum Hall Effect in 1980. In the last decade, new categories of topological insulators were predicted and later discovered, that have gained a lot of attraction for room-temperature applications. Since the experimental observation of single Dirac cone on the surface states of Bismuth selenide (Bi2Se3) in 2009, it has emerged as the prototype. Bismuth Selenide has one of the highest bulk band gaps of 0.3 eV among all TI materials. While its single crystal properties are well documented, thin films are producing equally exciting discoveries. In this work, Bi2Se3 thin films were synthesized using magnetron sputtering method and a diverse set of physical properties, such as structural, optical, and electronic, are investigated. In particular, properties of few-layer (ultra-thin) Bi2Se3 thin films are studied. Optical properties of Bi2Se3 was particularly revealing. We observed a sharp increase (blue shift) in the bulk band gap of Bi2Se3 by almost 0.5 eV as it approached the two-dimensional limit. Strong thickness-dependent structural and transport properties were also observed.

One of the most remarkable achievements of modern condensed matter physics is the discovery of topological phases of matter. Materials in a non-trivial topological phase or the topological insulators can be distinguished by their unique electronic and transport properties which are indifferent to different types of perturbations and thus open new routes towards the dissipationless transport. Explaining their properties requires proper involvement of relativistic approach as well as topological analysis. Among different classes of topological insulators, the Z2 topological insulators have drawn special attention due to their strong spin-orbit coupling which makes them a promising candidate for spintronics application, especially for magnetic memory devices. Due to their inherent strong spin-orbit coupling, they provide an efficient way to manipulate electronic spin with an applied electric field via spin orbit torque. The topological insulators have been found to be far more superior in manipulating the magnetic order parameter of a ferromagnet compared to the conventional heavy metals like platinum or tantalum. Another milestone in magnetic memory devices is marked by the introduction of antiferromagnetic memory devices which has not drawn any attention for long time as they cannot be controlled by an applied magnetic field. Recently it has been found that in case of a non-centrosymmetric antiferromagnet, the magnetic order parameter can be manipulated by with spin-orbit torque which also have been verified experimentally. The advantages of antiferromagnetic devices over ferromagnetic devices are that they allow faster switching speed and they are immune to an external magneticfield which are two highly solicited properties for next generation spintronic devices. This thesis is focused on understanding the transport properties in topologically nontrivial materials and their interface with different magnetic material. We use simplified continuum model as well as tight binding models to capture the salient features of these systems. Using non-equilibrium Green's function we explore their transport properties as well as spin-charge conversion mechanism. Our finding would provide a better understanding of these new class of materials and thus would be instrumental to discover new mechanisms to manipulate their properties.

The recent discoveries of topological insulators (TI) has opened a new realm for study¬ing topological systems and exploring the exotic properties they offer. The in-built topological protection against direct backscattering and absence of localization makes two-dimensional (2D) surface states of bismuth chalcogenide-based strong TI a promising platform for studying interesting phenomena in condensed matter physics like dissipation-less transport, quantum anomalous hall effect, topological magnetoelectric effect, majo¬rana fermions etc. and also makes this system very suitable for applications in the fields of electronics and spintronics. However, realization of these novel states can be difficult because of scattering of surface states from different types of disorders (intrinsic or ex¬trinsic) or the presence of parallel channels in the bulk of the sample which can dominate over surface transport. The main goal of this thesis is to evaluate the performance of TI as an electronic element and look into elastic and inelastic scattering processes and kinetics of these scatterers. In most part of this work we concentrate on the magnitude and origin of low-frequency flicker noise or the 1/f-noise, a key performance marker in electronics, to characterize the electrical transport in TI. In this work we have studied 1/f-noise in both mechanically exfoliated TI-flakes and epitaxially grown TI films by varying chemical potential and temperature. Our study of exfoliated TI-flakes with a wide range of thickness (10 nm to 80 μm) suggests that whereas at thinner (<100 nm) samples and at low temperature (<70 K), the electrical transport happens entirely at the surface, resistance fluctuations in the surface states are mainly caused by potential fluctuations caused by generation-recombination processes in the bulk of TI. Study of 1/f-noise in MBE-grown magnetically doped TI reveals signature of hopping transport through localized bulk mid gap states. These states can either be Cr-impurity band or disorder-induced mobility edge states of bulk valence band. Our study of quantum transport in exfoliated TI-devices indicate presence of a de-coherence mechanism which saturates phase-coherence length and temperature below T< 3 K and results from a unique scattering mechanism caused by localized magnetic moments in these systems

The topological insulator Bi2Te3 has been grown on Si(111)-(7 × 7) surface by molecular beam epitaxy. Reflection high energy electron diffraction, in situ scanning tunnelling microscopy, x-ray photoelectron spectroscopy and ex situ x-ray diffraction studies have been performed to analyze the quality of the growth. These analyses suggest a very good layer-by-layer epitaxial growth of Bi2Te3 on the atomically at Si surface. The magnetoresistance of the samples has been studied with magnetic field perpendicular and parallel to the sample surface, up to 9 T, over a temperature range of 2 K to 20 K. A sharp dip at low fields (0 T - 1 T) and near-linear behavior for high fields (> 4 T) have been observed in the perpendicular field magnetoresistance. The low field dip is due to weak antilocalization that agrees well with the simplified Hikami-Larkin-Nagaoka model. It has been demonstrated that both the low field dip and the high field near-linear behavior can be explained by the original Hikami-Larkin-Nagaoka formula alone in a system with strong spin-orbit coupling. From the fitting of the perpendicular field magnetoresistance the phase coherence length, the mean free path and the spin-orbit relaxation time have been estimated. The phase coherence length shows power law dependence with temperature indicating two dimensional nature of the transport. The power law also suggests electron electron interaction as the prominent dephasing mechanism. The out-of-plane spin-orbit relaxation time is determined to be small and the in-plane spin-orbit relaxation time is found to be comparable to the momentum relaxation time. The estimation of these charge and spin transport parameters is useful for topological insulator based magneto electric device applications. It also has been shown that the strong spin-orbit coupling suppresses the Zeeman contribution in perpendicular field magnetoresistance. The logarithmic divergence of perpendicular field magnetoresistance with temperature for low temperature range (2 K - 20 K) at high fields shows the presence of Coulomb interaction in the spin singlet channel. For magnetoresistance with the field parallel to the sample surface, the observed magnetoresistance has parabolic dependence for small fields (0 T - 0.6 T) and logarithmic dependence for large fields (> 3 T), which is due to the Zeeman effect. It is found that the data are inconsistent with only the Maekawa and Fukuyama theory of non interacting electrons with Zeeman contributions to the transport, but are consistent with theory if one also takes into account the electron electron interaction and the Zeeman splitting term in the electron electron interaction theory of Lee and Ramakrishnan. The Zeeman g-factor and the strength of Coulomb scattering due to electron electron interaction have been estimated from fitting of the parallel field magnetoresistance. The magnetoresistance also shows anisotropy with respect to the field directions. The angle dependent anisotropic magnetoresistance can be fitted well by the original HLN theory alone. The anisotropy can have potential application in anisotropic magnetic sensors. / text