Predicting a new phase (T′′) of two-dimensional transition metal di-chalcogenides and strain-controlled topological phase transition

Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T′′), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T′′ MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T′′ phase unambiguously display similar band topologies and strain controlled topological phase transitions. Our findings greatly enrich the 2D families of transition metal dichalcogenides and offer a feasible way to control the electronic states of 2D topological insulators for the fabrication of high-speed spintronics devices.

Transport across a junction of topological insulators and a superconductor

We study transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. The junction can have three time-reversal invariant barriers on three sides. We compute the charge and the spin conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters used to characterize the barrier. We find that the presence of topological insulators and a superconductor leads to both Dirac- and Schrodinger-like features in charge and spin conductances. We discuss the effect of bound states on the superconducting side of the barrier on the conductance; in particular, we show that for triplet p-wave superconductors, such a junction may be used to determine the spin state of its Cooper pairs. Our study reveals that there is a nonzero spin conductance for some particular spin states of the triplet Cooper pairs; this is an effect of the topological insulators which break the spin rotation symmetry. Finally, we find an unusual satellite peak (in addition to the usual zero bias peak) in the spin conductance for p-wave symmetry of the superconductor order parameter.

Electronic states in disordered topological insulators

We present a theoretical study of electronic states in topological insulators with impurities. Chiral edge states in 2d topological insulators and helical surface states in 3d topological insulators show a robust transport against nonmagnetic impurities. Such a nontrivial character inspired physicists to come up with applications such as spintronic devices [1], thermoelectric materials [2], photovoltaics [3], and quantum computation [4]. Not only has it provided new opportunities from a practical point of view, but its theoretical study has deepened the understanding of the topological nature of condensed matter systems. However, experimental realizations of topological insulators have been challenging. For example, a 2d topological insulator fabricated in a HeTe quantum well structure by Konig et al. [5] shows a longitudinal conductance which is not well quantized and varies with temperature. 3d topological insulators such as Bi₂Se₃ and Bi₂Te₃ exhibit not only a signature of surface states, but they also show a bulk conduction [6]. The series of experiments motivated us to study the effects of impurities and coexisting bulk Fermi surface in topological insulators. We first address a single impurity problem in a topological insulator using a semiclassical approach. Then we study the conductance behavior of a disordered topological-metal strip where bulk modes are associated with the transport of edge modes via impurity scattering. We verify that the conduction through a chiral edge channel retains its topological signature, and we discovered that the transmission can be succinctly expressed in a closed form as a ratio of determinants of the bulk Green's function and impurity potentials. We further study the transport of 1d systems which can be decomposed in terms of chiral modes. Lastly, the surface impurity effect on the local density of surface states over layers into the bulk is studied between weak and strong disorder strength limits.

Numerical Studies of Topological Phases

The topological phases of matter have been a major part of condensed matter physics research since the discovery of the quantum Hall effect in the 1980s. Recently, much of this research has focused on the study of systems of free fermions, such as the integer quantum Hall effect, quantum spin Hall effect, and topological insulator. Though these free fermion systems can play host to a variety of interesting phenomena, the physics of interacting topological phases is even richer. Unfortunately, there is a shortage of theoretical tools that can be used to approach interacting problems. In this thesis I will discuss progress in using two different numerical techniques to study topological phases.

Recently much research in topological phases has focused on phases made up of bosons. Unlike fermions, free bosons form a condensate and so interactions are vital if the bosons are to realize a topological phase. Since these phases are difficult to study, much of our understanding comes from exactly solvable models, such as Kitaev's toric code, as well as Levin-Wen and Walker-Wang models. We may want to study systems for which such exactly solvable models are not available. In this thesis I present a series of models which are not solvable exactly, but which can be studied in sign-free Monte Carlo simulations. The models work by binding charges to point topological defects. They can be used to realize bosonic interacting versions of the quantum Hall effect in 2D and topological insulator in 3D. Effective field theories of "integer" (non-fractionalized) versions of these phases were available in the literature, but our models also allow for the construction of fractional phases. We can measure a number of properties of the bulk and surface of these phases.

Few interacting topological phases have been realized experimentally, but there is one very important exception: the fractional quantum Hall effect (FQHE). Though the fractional quantum Hall effect we discovered over 30 years ago, it can still produce novel phenomena. Of much recent interest is the existence of non-Abelian anyons in FQHE systems. Though it is possible to construct wave functions that realize such particles, whether these wavefunctions are the ground state is a difficult quantitative question that must be answered numerically. In this thesis I describe progress using a density-matrix renormalization group algorithm to study a bilayer system thought to host non-Abelian anyons. We find phase diagrams in terms of experimentally relevant parameters, and also find evidence for a non-Abelian phase known as the "interlayer Pfaffian".

Signatures of Topological Superconductors

Topological superconductors are particularly interesting in light of the active ongoing experimental efforts for realizing exotic physics such as Majorana zero modes. These systems have excitations with non-Abelian exchange statistics, which provides a path towards topological quantum information processing. Intrinsic topological superconductors are quite rare in nature. However, one can engineer topological superconductivity by inducing effective p-wave pairing in materials which can be grown in the laboratory. One possibility is to induce the proximity effect in topological insulators; another is to use hybrid structures of superconductors and semiconductors.

The proposal of interfacing s-wave superconductors with quantum spin Hall systems provides a promising route to engineered topological superconductivity. Given the exciting recent progress on the fabrication side, identifying experiments that definitively expose the topological superconducting phase (and clearly distinguish it from a trivial state) raises an increasingly important problem. With this goal in mind, we proposed a detection scheme to get an unambiguous signature of topological superconductivity, even in the presence of ordinarily detrimental effects such as thermal fluctuations and quasiparticle poisoning. We considered a Josephson junction built on top of a quantum spin Hall material. This system allows the proximity effect to turn edge states in effective topological superconductors. Such a setup is promising because experimentalists have demonstrated that supercurrents indeed flow through quantum spin Hall edges. To demonstrate the topological nature of the superconducting quantum spin Hall edges, theorists have proposed examining the periodicity of Josephson currents respect to the phase across a Josephson junction. The periodicity of tunneling currents of ground states in a topological superconductor Josephson junction is double that of a conventional Josephson junction. In practice, this modification of periodicity is extremely difficult to observe because noise sources, such as quasiparticle poisoning, wash out the signature of topological superconductors. For this reason, We propose a new, relatively simple DC measurement that can compellingly reveal topological superconductivity in such quantum spin Hall/superconductor heterostructures. More specifically, We develop a general framework for capturing the junction's current-voltage characteristics as a function of applied magnetic flux. Our analysis reveals sharp signatures of topological superconductivity in the field-dependent critical current. These signatures include the presence of multiple critical currents and a non-vanishing critical current for all magnetic field strengths as a reliable identification scheme for topological superconductivity.

This system becomes more interesting as interactions between electrons are involved. By modeling edge states as a Luttinger liquid, we find conductance provides universal signatures to distinguish between normal and topological superconductors. More specifically, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as a lead. Interestingly, arbitrarily weak interactions induce qualitative changes in the behavior relative to the free-fermion limit, leading to a sharp dichotomy in conductance for the trivial (narrow superconductor) and topological (wide superconductor) cases. Furthermore, we find that strong interactions can in principle induce parafermion excitations at a superconductor/quantum spin Hall junction.

As we identify the existence of topological superconductor, we can take a step further. One can use topological superconductor for realizing Majorana modes by breaking time reversal symmetry. An advantage of 2D topological insulator is that networks required for braiding Majoranas along the edge channels can be obtained by adjoining 2D topological insulator to form corner junctions. Physically cutting quantum wells for this purpose, however, presents technical challenges. For this reason, I propose a more accessible means of forming networks that rely on dynamically manipulating the location of edge states inside of a single 2D topological insulator sheet. In particular, I show that edge states can effectively be dragged into the system's interior by gating a region near the edge into a metallic regime and then removing the resulting gapless carriers via proximity-induced superconductivity. This method allows one to construct rather general quasi-1D networks along which Majorana modes can be exchanged by electrostatic means.

Apart from 2D topological insulators, Majorana fermions can also be generated in other more accessible materials such as semiconductors. Following up on a suggestion by experimentalist Charlie Marcus, I proposed a novel geometry to create Majorana fermions by placing a 2D electron gas in proximity to an interdigitated superconductor-ferromagnet structure. This architecture evades several manufacturing challenges by allowing single-side fabrication and widening the class of 2D electron gas that may be used, such as the surface states of bulk semiconductors. Furthermore, it naturally allows one to trap and manipulate Majorana fermions through the application of currents. Thus, this structure may lead to the development of a circuit that enables fully electrical manipulation of topologically-protected quantum memory. To reveal these exotic Majorana zero modes, I also proposed an interference scheme to detect Majorana fermions that is broadly applicable to any 2D topological superconductor platform.

Response of the topological surface state to surface disorder in TlBiSe2

Through a combination of experimental techniques we show that the topmost layer of the topological insulator TlBiSe2 as prepared by cleavage is formed by irregularly shaped Tl islands at cryogenic temperatures and by mobile Tl atoms at room temperature. No trivial surface states are observed in photoemission at low temperatures, which suggests that these islands cannot be regarded as a clear surface termination. The topological surface state is, however, clearly resolved in photoemission experiments. This is interpreted as direct evidence of its topological self-protection and shows the robust nature of the Dirac cone-like surface state. Our results can also help explain the apparent mass acquisition in S-doped TlBiSe2.

Topological order in a broken-symmetry state

À travers cette thèse, nous revisitons les différentes étapes qui ont conduit à la découverte des isolants topologiques, suite à quoi nous nous penchons sur la question à savoir si une phase topologiquement non-triviale peut coexister avec un état de symétrie brisée. Nous abordons les concepts les plus importants dans la description de ce nouvel état de la matière, et tentons de comprendre les conséquences fascinantes qui en découlent. Il s’agit d’un champ de recherche fortement alimenté par la théorie, ainsi, l’étude du cadre théorique est nécessaire pour atteindre une compréhension profonde du sujet. Le chapitre 1 comprend un retour sur l’effet de Hall quantique, afin de motiver les sections subséquentes. Le chapitre 2 présente la première réalisation d’un isolant topologique à deux dimensions dans un puits quantique de HgTe/CdTe, suite à quoi ces résultats sont généralisés à trois dimensions. Nous verrons ensuite comment incorporer des principes de topologie dans la caractérisation d’un système spécifique, à l’aide d’invariants topologiques. Le chapitre 3 introduit le premier dérivé de l’état isolant topologique, soit l’isolant topologique antiferromagnétique (ITAF). Après avoir motivé théoriquement le sujet et introduit un invariant propre à ce nouvel état ITAF, qui est couplé à l’ordre de Néel, nous explorons, dans les chapitres 4 et 5, deux candidats de choix pour la phase ITAF : GdBiPt et NdBiPt.

Colossal anisotropy in diluted magnetic topological insulators

We consider dilute magnetic doping in the surface of a three dimensional topological insulator where a two dimensional Dirac electron gas resides. We find that exchange coupling between magnetic atoms and the Dirac electrons has a strong and peculiar effect on both. First, the exchange-induced single ion magnetic anisotropy is very large and favors off-plane orientation. In the case of a ferromagnetically ordered phase, we find a colossal magnetic anisotropy energy, of the order of the critical temperature. Second, a persistent electronic current circulates around the magnetic atom and, in the case of a ferromagnetic phase, around the edges of the surface.

New generation of two-dimensional spintronic systems realized by coupling of Rashba and Dirac fermions

Intriguing phenomena and novel physics predicted for two-dimensional (2D) systems formed by electrons in Dirac or Rashba states motivate an active search for new materials or combinations of the already revealed ones. Being very promising ingredients in themselves, interplaying Dirac and Rashba systems can provide a base for next generation of spintronics devices, to a considerable extent, by mixing their striking properties or by improving technically significant characteristics of each other. Here, we demonstrate that in BiTeI@PbSb2Te4 composed of a BiTeI trilayer on top of the topological insulator (TI) PbSb2Te4 weakly- and strongly-coupled Dirac-Rashba hybrid systems are realized. The coupling strength depends on both interface hexagonal stacking and trilayer-stacking order. The weakly-coupled system can serve as a prototype to examine, e.g., plasmonic excitations, frictional drag, spin-polarized transport, and charge-spin separation effect in multilayer helical metals. In the strongly-coupled regime, within similar to 100 meV energy interval of the bulk TI projected bandgap a helical state substituting for the TI surface state appears. This new state is characterized by a larger momentum, similar velocity, and strong localization within BiTeI. We anticipate that our findings pave the way for designing a new type of spintronics devices based on Rashba-Dirac coupled systems.

Étude de la phase isolant topologique chez le composé demi-Heusler GdBiPt.

Il sera question dans ce mémoire de maîtrise de l’étude d’une nouvelle classification des états solides de la matière appelée isolant topologique. Plus précisément, nous étudierons cette classification chez le composé demi-Heusler GdBiPt. Nous avons principalement cherché à savoir si ce composé ternaire est un isolant topologique antiferromagnétique. Une analyse de la susceptibilité magnétique ainsi que de la chaleur spécifique du maté- riau montre la présence d’une transition antiferromagnétique à 8.85(3) K. Une mesure d’anisotropie de cette susceptibilité montre que les plans de spins sont ordonnés sui- vant la direction (1,1,1) et finalement des mesures de résistivité électronique ainsi que de l’effet Hall nous indiquent que nous avons un matériau semimétallique lorsque nous sommes en présence d’antiferromagnétisme. Présentement, les expériences menées ne nous permettent pas d’associer cet état métallique aux états surfaciques issus de l’état d’isolant topologique.

Spin-filtered edge states in graphene

Spin–orbit coupling changes graphene, in principle, into a two-dimensional topological insulator, also known as quantum spin Hall insulator. One of the expected consequences is the existence of spin-filtered edge states that carry dissipationless spin currents and undergo no backscattering in the presence of non-magnetic disorder, leading to quantization of conductance. Whereas, due to the small size of spin–orbit coupling in graphene, the experimental observation of these remarkable predictions is unlikely, the theoretical understanding of these spin-filtered states is shedding light on the electronic properties of edge states in other two-dimensional quantum spin Hall insulators. Here we review the effect of a variety of perturbations, like curvature, disorder, edge reconstruction, edge crystallographic orientation, and Coulomb interactions on the electronic properties of these spin filtered states.

Edge states in graphene-like systems

The edges of graphene and graphene like systems can host localized states with evanescent wave function with properties radically different from those of the Dirac electrons in bulk. This happens in a variety of situations, that are reviewed here. First, zigzag edges host a set of localized non-dispersive state at the Dirac energy. At half filling, it is expected that these states are prone to ferromagnetic instability, causing a very interesting type of edge ferromagnetism. Second, graphene under the influence of external perturbations can host a variety of topological insulating phases, including the conventional quantum Hall effect, the quantum anomalous Hall (QAH) and the quantum spin Hall phase, in all of which phases conduction can only take place through topologically protected edge states. Here we provide an unified vision of the properties of all these edge states, examined under the light of the same one orbital tight-binding model. We consider the combined action of interactions, spin–orbit coupling and magnetic field, which produces a wealth of different physical phenomena. We briefly address what has been actually observed experimentally.

Tailoring of Electronic Structure and Thermoelectric Properties of a Topological Crystalline Insulator by Chemical Doping

Topological crystalline insulators (TCIs) are a new quantum state of matter in which linearly dispersed metallic surface states are protected by crystal mirror symmetry. Owing to its vanishingly small bulk band gap, a TCI like Pb0.6Sn0.4Te has poor thermoelectric properties. Breaking of crystal symmetry can widen the band gap of TCI. While breaking of mirror symmetry in a TCI has been mostly explored by various physical perturbation techniques, chemical doping, which may also alter the electronic structure of TCI by perturbing the local mirror symmetry, has not yet been explored. Herein, we demonstrate that Na doping in Pb0.6Sn0.4Te locally breaks the crystal symmetry and opens up a bulk electronic band gap, which is confirmed by direct electronic absorption spectroscopy and electronic structure calculations. Na doping in Pb0.6Sn0.4Te increases p-type carrier concentration and suppresses the bipolar conduction (by widening the band gap), which collectively gives rise to a promising zT of 1 at 856 K for Pb0.58Sn0.40Na0.02Te. Breaking of crystal symmetry by chemical doping widens the bulk band gap in TCI, which uncovers a route to improve TCI for thermoelectric applications.

Tetragonal bismuth bilayer: A stable and robust quantum spin hall insulator

Topological insulators (TIs) exhibit novel physics with great promise for new devices, but considerable challenges remain to identify TIs with high structural stability and large nontrivial band gap suitable for practical applications. Here we predict by first-principles calculations a two-dimensional (2D) TI, also known as a quantum spin Hall (QSH) insulator, in a tetragonal bismuth bilayer (TB-Bi) structure that is dynamically and thermally stable based on phonon calculations and finite-temperature molecular dynamics simulations. Density functional theory and tight-binding calculations reveal a band inversion among the Bi-p orbits driven by the strong intrinsic spin-orbit coupling, producing a large nontrivial band gap, which can be effectively tuned by moderate strains. The helical gapless edge states exhibit a linear dispersion with a high Fermi velocity comparable to that of graphene, and the QSHphase remains robust on a NaCl substrate. These remarkable properties place TB-Bi among the most promising 2D TIs for high-speed spintronic devices, and the present results provide insights into the intriguing QSH phenomenon in this new Bi structure and offer guidance for its implementation in potential applications.

Broken symmetry and strangeness of the semiconductor impurity band metal-insulator transition

The filamentary model of the metal-insulator transition in randomly doped semiconductor impurity bands is geometrically equivalent to similar models for continuous transitions in dilute antiferromagnets and even to the λ transition in liquid He, but the critical behaviors are different. The origin of these differences lies in two factors: quantum statistics and the presence of long range Coulomb forces on both sides of the transition in the electrical case. In the latter case, in addition to the main transition, there are two satellite transitions associated with disappearance of the filamentary structure in both insulating and metallic phases. These two satellite transitions were first identified by Fritzsche in 1958, and their physical origin is explained here in geometrical and topological terms that facilitate calculation of critical exponents.