Download or read book Electronic Transport in Tunnel Junctions of Quantum Spin Hall Effect Topological Insulators written by Pietro Sternativo and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topological Insulators written by C. Brüne and published by Elsevier Inc. Chapters. This book was released on 2013-11-23 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This chapter will focus on the experimental properties of the quantum spin Hall effect in HgTe quantum well structures. HgTe quantum wells above a critical thickness are 2-dimensional topological insulators. The most prominent signature of the non-trivial topology in these systems is the occurrence of the quantum spin Hall effect when the Fermi energy is located inside the bulk band gap. We will present the main experimental results we obtained for transport in the quantum spin Hall regime and discuss how they confirm the prediction of the quantum spin Hall effect as a helical edge state system consisting of two counterpropagating oppositely spin polarized edge states.
Download or read book Topological Insulators written by Joel E. Moore and published by Elsevier Inc. Chapters. This book was released on 2013-11-23 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the topological insulator phase that emerges via spin-orbit coupling in three-dimensional materials is introduced, stressing its relationship to earlier topological phases in two dimensions. An unusual surface state with an odd number of “Dirac points” appears as a consequence of bulk topological invariants of the band structure. A different theoretical approach is then presented, based on the Berry phase of Bloch electrons, in order to illustrate a deep connection to the orbital contribution to the magnetoelectric polarizability in all materials. The unique features of transport in the topological insulator surface state are reviewed with an emphasis on possible experiments. The final section discusses briefly connections to interacting phases including topological superconductors and some recent efforts to construct fractional topological insulators in three dimensions.
Download or read book Topological Insulators written by Gregory Tkachov and published by CRC Press. This book was released on 2015-10-14 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of dynamic developments that have occurred in condensed matter physics after the recent discovery of a new class of electronic materials: topological insulators. A topological insulator is a material that behaves as a band insulator in its interior, while acting as a metallic conductor at its surface. The surface current car
Download or read book Studies on Time reversal Invariant Topological Insulators written by Joseph Maciejko and published by Stanford University. This book was released on 2011 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation brings together a number of topics in the theory of time-reversal invariant topological insulators. The first four chapters are devoted to the transport properties of the two-dimensional (2D) quantum spin Hall state. We explain nonlocal transport measurements in mercury telluride (HgTe) quantum wells in terms of a Landauer-Büttiker theory of helical edge transport and confirm the discovery of the quantum spin Hall state in this material. We find that decoherence can lead to backscattering without breaking microscopic time-reversal symmetry. As an example of incoherent scattering, we study a Kondo impurity in an interacting helical edge liquid. A renormalization group analysis shows the existence of an impurity quantum phase transition governed by the Luttinger parameter of the edge liquid between a local helical Fermi liquid with T^6 scaling of the low-temperature conductance, and an insulating strongly correlated phase with fractionally charged emergent excitations. In the presence of a time-reversal symmetry breaking magnetic field, it is known that even coherent scattering can lead to backscattering. Through exact numerical diagonalization we find that nonmagnetic quenched disorder has a strong localizing effect on the edge transport if the disorder strength is comparable to the bulk gap. The predicted magnetoconductance agrees qualitatively with experiment. The last two chapters are devoted to 3D topological insulators. We propose a combined magnetooptical Kerr and Faraday rotation experiment as a universal measure of the Z_2 invariant. Finally, we propose a fractional generalization of 3D topological insulators in strongly correlated systems, characterized by ground state degeneracy on topologically nontrivial spatial 3-manifolds, a quantized fractional bulk magnetoelectric polarizability without time-reversal symmetry breaking, and a halved fractional quantum Hall effect on the surface.
Download or read book Topological Insulators written by Vadim Nemytov and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "In this thesis we investigate quantum transport properties of topological insulator (TI) Bi2 Se3 from atomistic point of view. TI is a material having an energy gap in its bulk but supporting gapless helical states on its boundary. The helical states have Dirac-like linear energy dispersion continuously crossing the bulk band gap with a spin texture in which the electron spin is locked perpendicular to the electron momentum. The peculiar electronic structure of TI material Bi2 Se3 is due to a strong spin-orbit interaction and is protected by the time reversal symmetry. The thesis consists of two main parts. The first reviews the theory of TI and the second presents our atomistic calculations of electron transport in the Bi2 Se3 material. In the theoretical review of the physics of TI, I follow the literature and attempt to present it in a reasonably accessible manner. The theory of TI is explained in terms of well known physical phenomena including classical and quantum Hall effects, spin-orbit coupling, spin current, and spin-Hall effect. The concept of Berry's phase is then introduced to link with the formal conventionalclassification of TI by the topological Z2 invariants. The entire discussion is within the well known Bloch band theory. In the second part of this thesis, numerical studies of transport properties of Bi2 Se3 are presented. After a brief discussion of the relevant quantum transport theory and the tight binding atomistic model, we present our calculated quantum transport results of Bi2 Se3 films having a trench in the middle. Such a large defect, if on normal conductors, would cause significant back scattering of the carriers. Here, by topological protection of the helical states, back scattering is forbidden due to the spin-momentum locking. Nevertheless, large trenches in the film may cause the helical states on the surface to mix inside the trench, thereby affecting the transmission." --
Download or read book Quantum Electronic Transport in Atomically Layered Topological Insulators written by Valla Fatemi and published by . This book was released on 2018 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The merger of topology and symmetry established a new foundation for understanding the physics of condensed matter, beginning with the notion of topological insulators (TIs) for electronic systems. For the time-reversal invariant TIs, a key aspect is the "helical" mode at the boundary of the system - that is, the ID edge of a 2D topological insulator or the 2D surface of a 3D topological insulator. These helical modes represent the extreme limit of spin-orbit coupling in that the spin-degenercy has been completely lifted while preserving time-reversal symmetry. This property is crucial for proposals realizing exotic excitations like the Majorana bound state. In this thesis, I present a series of experiments investigating electronic transport through the boundary modes of 3D and 2D topological insulators, specifically Bi1.5 Sb0.5 Te1.7 Se1.3 and monolayer WTe 2 , respectively. For the case of ultra-thin WTe 2 , I also present experiments detailing investigations of the 2D bulk states, finding a semimetallic state for the trilayer and a superconducting phase for the monolayer, both of which are strongly tunable by the electric field effect. The discovery of 2D topological insulator and 2D superconductor phases within the same material, accessible by standard solid state elecrostatic gates, places WTe2 in a unique situation among both TIs and superconductors, potentially enabling gate-configurable topological devices within a homogenous material platform.
Download or read book Topological Insulators written by Naoto Nagaosa and published by Elsevier Inc. Chapters. This book was released on 2013-11-23 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery of the rich topological structures of electronic states in solids has opened up many interesting possibilities. The “twist” of the wavefunctions in momentum space, which is characterized by topological invariants, leads to the robust edge or surface states. The electron fractionalization associated with these topological states brings about the novel physics such as absence of localization, topological magneto-electric effect, and Majorana fermions. Here we describe the principles and some concrete examples of the theoretical design of the topological materials and their functions based on these recent developments.
Download or read book Topological Insulators written by Shun-Qing Shen and published by Springer Science & Business Media. This book was released on 2013-01-11 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological insulators are insulating in the bulk, but process metallic states present around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, the first of its kind on topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological insulators and related areas. Shun-Qing Shen is a Professor at the Department of Physics, the University of Hong Kong, China.
Download or read book Spintronics Handbook Second Edition Spin Transport and Magnetism written by Evgeny Y. Tsymbal and published by CRC Press. This book was released on 2019-05-20 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition offers an update on the single most comprehensive survey of the two intertwined fields of spintronics and magnetism, covering the diverse array of materials and structures, including silicon, organic semiconductors, carbon nanotubes, graphene, and engineered nanostructures. It focuses on seminal pioneering work, together with the latest in cutting-edge advances, notably extended discussion of two-dimensional materials beyond graphene, topological insulators, skyrmions, and molecular spintronics. The main sections cover physical phenomena, spin-dependent tunneling, control of spin and magnetism in semiconductors, and spin-based applications.
Download or read book Advanced Topological Insulators written by Huixia Luo and published by John Wiley & Sons. This book was released on 2019-03-12 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for researchers and graduate students preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with the fundamental description on the topological phases of matter such as one, two- and three-dimensional topological insulators, and methods and tools for topological material's investigations, topological insulators for advanced optoelectronic devices, topological superconductors, saturable absorber and in plasmonic devices. Advanced Topological Insulators provides researchers and graduate students with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.
Download or read book Topological Insulators written by C.L. Kane and published by Elsevier Inc. Chapters. This book was released on 2013-11-23 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: We give a pedagogical introduction to theory of topological insulators. Following an introduction to the role of topology in band theory, we discuss several examples in detail. These include theories of the electric polarization in one dimension, the integer quantum Hall effect in two dimensions and topological insulators in two and three dimensions. We close with a brief discussion of topological crystalline insulators, nodal semimetals, topological superconductivity and topological defects.
Download or read book Effective Continuous Model on Topological Insulators written by Wenyu Shan and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Effective Continuous Model on Topological Insulators" by Wenyu, Shan, 单文语, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Topological insulators are electronic materials that have a conventional energy gap as an insulator or semiconductor in the bulk, but possess gapless conducting states around their boundary. They are novel topological states of quantum matters and exhibit a series of exotic physics, such as quantum spin Hall effect, single valley Dirac fermions, Majorana fermions, topological magnetoelectric effect, etc. The conducting edge and surface states have topological origin of the electron band structure, and are protected by time-reversal symmetry such that they are robust or immune against local perturbation. In this dissertation, an effective continuous model for surface states is established from the three-dimensional modified Dirac model, and a theory of ultrathin film for topological insulators is developed. The established electronic model helps us explore spin physics of massive Dirac fermions. The theory has been successfully applied to explain an energy gap opening of the surface states in Bi2Se3 thin film in the measurement of angle-resolved photoemission spectroscopy (ARPES). In-gap bound states are also considered due to vacancy and impurity in topological insulators. It is found that a vacancy can always induce in-gap bound states in both two- and threedimensional topological insulators, and a half quantum magnetic flux inside the vacancy can result in helical Dirac zero modes. Finally the effect of random impurities on the surface transport in topological insulators is investigated, particularly the weak anti-localization of surface electrons in the quantum diffusion regime. It is found that the spin-orbit scattering may suppress the weak localization behaviors of massive Dirac fermions, which suggests an experiment to detect the weak localization in the topological insulator thin film. DOI: 10.5353/th_b4961767 Subjects: Condensed matter
Download or read book Signatures of Topological Superconductors written by Shu-Ping Lee and published by . This book was released on 2015 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Optical and Electrical Properties of Topological Insulator Bi2Se3 written by Jiajun Zhu and published by Anchor Academic Publishing. This book was released on 2017-07 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological insulator is one of the hottest research topics in solid state physics. This is the first book to describe the vibrational spectroscopies and electrical transport of topological insulator Bi2Se3, one of the most exciting areas of research in condensed matter physics. In particular, attempts have been made to summarize and develop the various theories and new experimental techniques developed over years from the studies of Raman scattering, infrared spectroscopy and electrical transport of topological insulator Bi2Se3. It is intended for material and physics researchers and graduate students doing research in the field of optical and electrical properties of topological insulators, providing them the physical understanding and mathematical tools needed to engage research in this quickly growing field. Some key topics in the emerging field of topological insulators are introduced.
Download or read book Quantum Edge Transport in Topological Insulators written by Andrew J. Bestwick and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the quantum Hall effect, electrons circulate in one direction around the edge of a 2D sample. The robustness of these states is protected by the topology of the band structure and scattering is only possible if thermally-activated 2D conduction provides a path across the bulk. However, the environmental conditions required for the effect (large magnetic fields and, usually, low temperatures) make it unsuitable for most practical applications. This dissertation discusses the implementation of two similar topological transport phenomena, in the absence of magnetic fields, using the class of materials known as topological insulators. First, it reports on investigations into the quantum spin Hall effect, a time-reversal-symmetric state with counterpropagating, spin-polarized edge channels. Mean free paths in this case are limited to only a few micrometers due to a scattering mechanism under investigation. Second, it reports on recent results on the quantum anomalous Hall effect demonstrating part-per-10,000 conductance quantization, arising from nearly perfect transport through one-way edge channels, in magnetically-doped thin films of 3D topological insulators. It shows that dissipation only occurs due to thermally-activated states that can be nearly eliminated via an unexpected magnetocaloric effect.
Download or read book Quantum Transport in 2 and 3 Dimensional Topological Insulators written by Di Xiao and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological insulators are materials that are insulating in the bulk but that conduct via topologically protected states on the boundary. The concept of topology in condensed matter physics was first introduced to explain the integer quantum Hall (IQH) effect. The perfect quantization of these topologically protected edge states, insensitive to sample geometry and disorder, stimulated an extensive search for many exciting new topological materials. One of the milestones along the journey was the theoretical prediction and experimental discovery of Z2 topological insulators.The first class of Z2 topological insulators discovered was the 2-dimensional topological insulator (2D TI), also known as the quantum spin Hall (QSH) insulator. The 2D TI can be viewed as a variation of the IQH system but with time-reversal-symmetry (TRS). The topological invariant for a 2D TI is the Z2 number, defined by its nontrivial band structure instead of the Chern number in the IQH case. Generalizing this idea to 3 dimensions led to the discovery of the 3D TI with four Z2 invariants. Both the 2D and 3D TIs are of interest as model platforms for testing theoretical problems of fundamental interest. For instance, they allow us to realize artificial condensed matter analogs of fundamental particles such as Majorana fermions and axions that have yet to be observed in nature. They are also of interest for potential technological applications, principally spintronics and quantum computing.This dissertation focuses on the synthesis, characterization, and transport properties of both 2D and 3D TIs. We first discuss the 2D TI candidate material system, type II InAs/GaSb quantum wells, which exhibits a rich topological phase diagram that can be tuned by several parameters such as sample geometry or electrostatic gating. By changing the thicknesses of relevant layers, we are able to enter a new insulating regime where unexpected high-density quantum oscillations are observed. We elucidate this phenomenon through theoretical calculation and through control experiments. The seemingly controversial coexistence of high density states and the insulating regime can be explained by the effect of the attractive Coulomb interaction, which was not considered in earlier theories.The second topic we address is quantum transport in 3D TI systems. Breaking the TRS of the 3D TI surface states leads to many exotic phenomena, including the quantum anomalous Hall (QAH) effect and the axion insulator state. By constructing a sandwich heterostructure that has different magnetic coercive fields in the top and bottom magnetic layers, while keeping the center layer free from magnetic impurities, both the QAH and the axion insulator state can be observed in low-temperature transport measurements, when the magnetization alignment of the top and bottom layers is parallel and antiparallel, respectively. We also discuss the scaling behavior of the topological quantum phase transition between these two states.
