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Author: Di Xiao
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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.
Author: Di Xiao
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
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.
Author: Joel E. Moore
Publisher: Elsevier Inc. Chapters
ISBN: 0128086831
Category : Science
Languages : en
Pages : 31
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Book Description
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.
Author: Louis Veyrat
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Gregory Tkachov
Publisher: CRC Press
ISBN: 9814613266
Category : Science
Languages : en
Pages : 180
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Book Description
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
Author: Jianxiao Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The discovery of topological states of matters has sparked intense interests amongresearchers in the past decade. Topologically non-trivial band structure in thesequantum states can give rise to a variety of topological phenomena, the experimentaldemonstration of which can have a huge impact on our understandingof fundamental states of matter. Transport measurement is one of the majorexperimental techniques to probe these topological phenomena. This dissertationis devoted to theoretical and numerical studies of quantum transport phenomenain a variety of topological materials, including magnetic topological insulator films,the quantum anomalous Hall insulator/superconductor hetero-structures, the kinkstates in bilayer graphene and the photonic crystal of topological mirror insulatorphase in the optical regime. The numerical simulations of transport phenomenaand the analytical understanding of the underlying physical mechanism in thisdissertation will provide guidance for the future transport measurements.The numerical methods to simulate quantum transport in this dissertation arebased on Landauer-Bttiker formalism and Greens function method, which willbe introduced in Chapter 2. The transmission through certain sample regionscan be extracted from the Greens function method and serves as the input forthe Landauer-Bttiker formalism to compute conductance tensor that is directlymeasured in transport experiments. Physical understanding of the transportmechanism can be provided by analyzing different components of the transmissionmatrix, in combination with other analytical methods for transport phenomena.Defects and impurities can be incorporated in numerical simulations by includingrandom potentials into the model Hamiltonian, and thus this method can be appliedin different transport regimes, from ballistic to diffusive transport.Chapter 3 to 5 of the dissertation is to apply the above numerical methodsto three different topological mesoscopic systems: magnetic topological insulator(MTI) films, quantum anomalous Hall insulator (QAHI) - superconductor (SC)junctions, and bilayer graphene devices.Chapter 3 is dedicated to the study of quantum transport through magnetictextures in a thin film of MTI. We focus on both the longitudinal and Hall transports,which reveal complicated features due to the coexistence of strong spin-orbit couplingfrom TI materials and magnetic non-colinearity from magnetic textures in thissystem. The manifested Hall transport can be induced by different topologicalmechanisms, including the intrinsic anomalous Hall effect from strong SOC and thetopological Hall effect (or known as geometric Hall effect) from magnetic textures.Thus, this system provides a nice platform to understand the interplay betweenspin-orbit coupling and real-space magnetic texture, as well as disorder scatterings.Our numerical simulations have shown different roles of spin-orbit coupling in theclean and disordered limits for this system. In the clean limit when SOC strengthis increased, the topological Hall conductance (THC) almost remains constant butthe topological Hall resistance (THR) can increase by an order of magnitude dueto the reduction of longitudinal conductance, caused by SOC-induced spin flips.However, in the disordered limit, both the THC and THR increase with increasingSOC, while longitudinal conductance is not influenced much by SOC.In Chapter 4, we study the transport of chiral edge channels in a QAHI/superconductorjunction. This type of hetero-junction has been recently fabricated andmeasured in experiments, in pursue of topological superconductivity and Majoranafermions. We focus on the disorder effect in the weak superconductor proximitylimit. Our results show that the quantized valued of conductance remains robustfor a single chiral edge channel even in the presence of disorder in the zero-biaslimit. However, such quantization is broken down for a finite bias, or for multiplechiral edge modes, or for the coexistence of a single chiral edge mode with othertrivial metallic modes, when disorders are present. Our theory provides guidanceto understand transport phenomena in these systems for future experiments.Chapter 5 is a simulation of transport behaviors through the so-called kinkstates in a bilayer graphene device under external electric and magnetic fields. Thedevice, known as a valley valve and electron beam splitter, has been fabricatedby our experimental collaborators and its unusual transport properties have beenmeasured experimentally. Our numerical simulations provide a justification of theguiding center physical picture for topological transport through this device.Chapter 6 goes beyond electronic systems and concerns topological phase inphotonic systems. We utilize a method of dynamic evolution of states to studya topological crystalline insulator phase in a photonic system. The crystallineprotection, achieved by the fine manufacturing of emulated atoms in a photoniclattice, selectively pumps incident states with a certain parity while reflects theother.The studies in the dissertation are in close collaboration with experimentalgroups, including Prof. Moses Chans and Prof. Cui-zu Changs group for the transportmeasurements in MTI films and QAHI/SC junctions, Prof. Jun Zhus groupfor the experiments on the bilayer graphene device, and Prof. Mikael Rechtsmansgroup for the photonic topological systems.
Author: B. Andrei Bernevig
Publisher: Princeton University Press
ISBN: 1400846730
Category : Science
Languages : en
Pages : 264
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Book Description
This graduate-level textbook 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 graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.
Author: Run Xiao
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This dissertation focuses on the synthesis, characterization, fabrication, and electrical transport measurements of topological materials, including magnetically doped topological insulators and Dirac semimetal Cd3As2. Bismuth-chalcogenide topological insulators have time-reversal-symmetry-protected surface states due to the strong spin-orbit coupling. Breaking the time-reversal symmetry by magnetic dopants can lead to fascinating exotic phenomena, such as the quantum anomalous Hall effect. On the other hand, Dirac semimetals host three-dimensional Dirac fermions and can be identified as a parent phase of other topological phases, such as Weyl semimetals. In this dissertation, quantum transport measurements are performed on thin films of topological materials to investigate and understand the unusual electronic states that host these topological phases. These studies can motivate and facilitate the development of potential applications of topological materials, especially in spintronics and quantum computing. The first topological material studied in this dissertation is a magnetically doped topological insulator system: Cr doped (Bi,Sb)2Te3 - (Bi,Sb)2Te3 - Cr doped (Bi,Sb)2Te3 sandwich heterostructure. By tuning the chemical and asymmetric potentials using dual gates, both the quantum anomalous hall effect, due to the topology in the momentum space, and the topological Hall effect, due to the topology in real space, can be observed in this heterostructure system. We also mapped out a phase diagram of the topological Hall and quantum anomalous Hall effects as a function of the chemical and asymmetry potentials, paving a way to understand and manipulate the chiral magnetic spin textures in real space. The second topological material is Dirac semimetal Cd3As2. We investigated the integer quantum Hall effect in Cd3As2 thin films under strong to moderate quantum confinement (thicknesses of 10 nm, 12 nm, and 15 nm). In all the films, we observed the integer quantum Hall effect in the spin-polarized lowest Landau level (filling factor [nu]=1) and at spin-degenerate higher index Landau levels with even filling factors ([nu]=2,4,6). We also observed the lifting of the Landau level spin degeneracy at v=3 with strong quantum confinement. A tight-binding calculation suggests that the enhanced g-factor due to the quantum confinement and corrections from nearby subbands can be the reason for the emergence of v=3 quantum Hall plateau. Last, we explored the introduction of the transition metal Mn into Cd3As2 thin films to break the time-reversal symmetry. Scanning transmission electron microscopy of these films shows a formation of an Mn-rich layer on top of a pure Cd3As2 layer using both uniform and delta doping methods. The low solubility of Mn in Cd3As2 can be the reason for the phase separation. The Mn-rich region shows out-of-plane magnetic anisotropy in superconducting quantum interference device magnetometry measurements. Moreover, the presence of the Mn surfactant lowers the carrier density in the Cd3As2 layer, and an incipient quantum Hall effect can be observed in low-temperature transport measurements.
Author:
Publisher: Academic Press
ISBN: 0323915108
Category : Science
Languages : en
Pages : 240
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Book Description
Topological Insulator and Related Topics, Volume 108 in the Semiconductors and Semimental series, highlights new advances in the field, with this new volume presenting interesting chapters on topics such as Majorana modes at the ends of one dimensional topological superconductors, Optical/electronic properties of Weyl semimetals, High magnetic fields to unveil the electronic structure, magnetic field-induced transitions, and unconventional transport properties of topological semimetals, New aspects of strongly correlated superconductivity in the nearly flat-band regime, Anomalous transport properties in topological semimetals, Pseudo-gauge field and piezo-electromagnetic response in topological materials, Topological Gapped States Protected by Spatial Symmetries, and more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Semiconductors and Semimetals series Updated release includes the latest information on Topological Insulator and Related Topics
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Huixia Luo
Publisher: John Wiley & Sons
ISBN: 111940732X
Category : Technology & Engineering
Languages : en
Pages : 400
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Book Description
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.
