Download or read book Quantum Transport in Topological Phases of Matter written by Michal Papaj and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological phases of matter attract constant attention in the condensed matter physics community, both due to the fundamental yet simple principles that govern them, and a multitude of experimental observations with the potential for technological applications. Among the ways of studying such materials, quantum transport methods prove to be of particular importance. In this thesis, I touch upon many aspects of quantum transport in topological materials. First, I introduce a novel type of Hall effect, called Magnus Hall effect, that allows one to probe Berry curvature in ballistic, time-reversal invariant systems that break inversion symmetry. Next, I present a detailed characterization of extrinsic Nernst effect in Dirac and Weyl semimetals, providing interpretation of existing experimental results and predictions for new enhanced responses in materials such as Fe3Sn2. In the following section, I demonstrate that a strong disorder can lead to a novel behavior of Dirac fermions in surface states of topological crystalline insulators, resulting in appearance of nodal arcs in place of Dirac points and in tilting of the Dirac cone. In the second part of the thesis, I focus on topological superconductors, starting by presenting a new method for creating Majorana zero modes using segmented Fermi surface. This approach, based on the Fermi surface of Bogoliubov quasiparticles allows for the reduction of the magnetic field required to induce a topological phase transition and reduces the number of spurious, low energy modes that hamper observation and utilization of Majorana zero modes. Finally, I show that the presence of multiple Majorana modes in a strongly correlated superconducting island leads to Kondo-like behavior with a topological twist.
Download or read book Topological Phases of Matter written by Roderich Moessner and published by Cambridge University Press. This book was released on 2021-04-29 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.
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 Topological Matter written by Dario Bercioux and published by Springer. This book was released on 2018-10-03 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers basic and advanced aspects in the field of Topological Matter. The chapters are based on the lectures presented during the Topological Matter School 2017. It provides graduate level content introducing the basic concepts of the field, including an introductory session on group theory and topological classification of matter. Different topological phases such as Weyls semi-metals, Majoranas fermions and topological superconductivity are also covered. A review chapter on the major experimental achievements in the field is also provided. The book is suitable not only for master, graduate and young postdoctoral researchers, but also to senior scientists who want to acquaint themselves with the subject.
Download or read book QUANTUM TRANSPORT IN TOPOLOGICAL MATERIALS written by Run Xiao and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topological Phases of Matter written by Roderich Moessner and published by Cambridge University Press. This book was released on 2021-04-29 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological Phases of Matter are an exceptionally dynamic field of research: several of the most exciting recent experimental discoveries and conceptual advances in modern physics have originated in this field. These have generated new, topological, notions of order, interactions and excitations. This text provides an accessible, unified and comprehensive introduction to the phenomena surrounding topological matter, with detailed expositions of the underlying theoretical tools and conceptual framework, alongside accounts of the central experimental breakthroughs. Among the systems covered are topological insulators, magnets, semimetals, and superconductors. The emergence of new particles with remarkable properties such as fractional charge and statistics is discussed alongside possible applications such as fault-tolerant topological quantum computing. Suitable as a textbook for graduate or advanced undergraduate students, or as a reference for more experienced researchers, the book assumes little prior background, providing self-contained introductions to topics as varied as phase transitions, superconductivity, and localisation.
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.
Download or read book Topology in Condensed Matter written by Michael I. Monastyrsky and published by Springer Science & Business Media. This book was released on 2006-02-04 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.
Download or read book Nonequilibrium Quantum Transport Theory Of Spinful And Topological Systems A New Perspective And Foundation For Topotronics written by Felix A Buot and published by World Scientific. This book was released on 2024-04-23 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book employs nonequilibrium quantum transport, based on the use of mixed Hilbert space representations and real time quantum superfield transport theory, to explain various topological phases of systems with entangled chiral degrees of freedom. It presents an entirely new perspective on topological systems, entanglement-induced localization and delocalization, integer quantum Hall effect (IQHE), fractional quantum Hall effect (FQHE), and its respective spectral zones in the Hofstadter butterfly spectrum. A simple and powerful, intuitive, and wide-ranging perspective on chiral transport dynamics.
Download or read book A Short Course on Topological Insulators written by János K. Asbóth and published by Springer. This book was released on 2016-02-22 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.
Download or read book Introduction to Topological Quantum Matter Quantum Computation written by Tudor D. Stanescu and published by CRC Press. This book was released on 2024-07-02 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid-state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture and emphasizing two major new paradigms in condensed matter physics – quantum topology and quantum information – this book is ideal for graduate students and researchers entering this field, as it allows for the fruitful transfer of ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and unveils the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the toric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Topological quantum computation is also presented using a broad perspective, which includes elements of classical and quantum information theory, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and key ideas underlying quantum computation with anyons. This new edition has been updated throughout, with exciting new discussions on crystalline topological phases, including higher-order topological insulators; gapless topological phases, including Weyl semimetals; periodically-driven topological insulators; and a discussion of axion electrodynamics in topological materials. Key Features: · Provides an accessible introduction to this exciting, cross-disciplinary area of research. · Fully updated throughout with new content on the latest result from the field. · Authored by an authority on the subject. Tudor Stanescu is a professor of Condensed Matter Theory at West Virginia University, USA. He received a B.S. in Physics from the University of Bucharest, Romania, in 1994 and a Ph.D. in Theoretical Physics from the University of Illinois at Urbana Champaign in 2002. He was a Postdoctoral Fellow at Rutgers University and at the University of Maryland from 2003 to 2009. He joined the Department of Physics and Astronomy at West Virginia University in Fall 2009. Prof. Stanescu’s research interests encompass a variety of topics in theoretical condensed matter physics including topological insulators and superconductors, topological quantum computation, ultra-cold atom systems in optical lattices, and strongly correlated materials, such as, for example, cuprate high-temperature superconductors. His research uses a combination of analytical and numerical tools and focuses on understanding the emergence of exotic states of matter in solid state and cold atom structures, for example, topological superconducting phases that host Majorana zero modes, and on investigating the possibilities of exploiting these states as physical platforms for quantum computation.
Download or read book Topological Insulators and Topological Superconductors written by B. Andrei Bernevig and published by Princeton University Press. This book was released on 2013-04-07 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quantum Transport in Topological Matter written by Jorrit Cornelis de Boer and published by . This book was released on 2019 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Physics and Bulk Boundary Correspondence in Topological Phases of Matter written by Abhijeet Alase and published by Springer Nature. This book was released on 2019-11-20 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis extends our understanding of systems of independent electrons by developing a generalization of Bloch’s Theorem which is applicable whenever translational symmetry is broken solely due to arbitrary boundary conditions. The thesis begins with a historical overview of topological condensed matter physics, placing the work in context, before introducing the generalized form of Bloch's Theorem. A cornerstone of electronic band structure and transport theory in crystalline matter, Bloch's Theorem is generalized via a reformulation of the diagonalization problem in terms of corner-modified block-Toeplitz matrices and, physically, by allowing the crystal momentum to take complex values. This formulation provides exact expressions for all the energy eigenvalues and eigenstates of the single-particle Hamiltonian. By precisely capturing the interplay between bulk and boundary properties, this affords an exact analysis of several prototypical models relevant to symmetry-protected topological phases of matter, including a characterization of zero-energy localized boundary excitations in both topological insulators and superconductors. Notably, in combination with suitable matrix factorization techniques, the generalized Bloch Hamiltonian is also shown to provide a natural starting point for a unified derivation of bulk-boundary correspondence for all symmetry classes in one dimension.
Download or read book Many Body Quantum Theory in Condensed Matter Physics written by Henrik Bruus and published by Oxford University Press. This book was released on 2004-09-02 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.
Download or read book Topological Quantum Materials written by Grigory Tkachov and published by CRC Press. This book was released on 2022-08-18 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: In topological quantum materials, quantum effects emerge at macroscopic scales and are robust to continuous changes in a material’s state. This striking synergy between quantum and topological properties is of great interest for both fundamental research and emerging technologies, especially in the fields of electronics and quantum information. This edition of the book presents a wealth of topological quantum materials, bringing together burgeoning research from different areas: topological insulators, transition metal dichalcogenides, Weyl semimetals, and unconventional and topological superconductors. The realization of the application potential of topological quantum materials requires understanding their properties at a fundamental level. This brings us back to the discovery of topological phases of matter, which earned the Nobel Prize in Physics in 2016. This book explores the connection between pioneering work on topological phases of matter and a flurry of activity that followed. The topics covered include the quantum anomalous and spin Hall effects, emergent axion electrodynamics and topological magnetoelectric effects, Weyl nodes and surface Fermi arcs, weak antilocalization, induced triplet superconductivity, Majorana fermion modes, and the fractional Josephson effect.
Download or read book Charge and Heat Transport in Topological Systems written by Flavio Ronetti and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, I address the intriguing and appealing topic of charge and heat transport in quantum Hall systems, which are among the most famous example of topological phases of matter, in presence of external time-dependent voltages. Quantum Hall effect occurs in two-dimensional electron systems in the limit of strong perpendicular magnetic fields. The hallmark of quantum Hall systems is the emergence of one-dimensional metallic edge states on the boundary. Along these edge states particles propagate with a definite direction. The coherence length ensured by topological protection guarantees to access wave-like nature of electrons. This properties inspired a new field of research, known as electron quantum optic. Single-electron source can be realized by applying to a quantum Hall system a periodic train of Lorentzian-shaped pulses.Plateaus of the Hall resistance appear also at fractional values of the resistance quantum. The physical explanation of fractional quantum Hall effect cannot neglect the correlation between electrons and this phase of matter is inherently strongly-correlated. By considering the application of a periodic train of Lorentzian pulses to a quantum Hall system, I investigate the charge density of a state composed by many levitons in the fractional quantum Hall regime, thus finding that it is re-arranged into a regular pattern of peaks and valleys, reminiscent of Wigner crystallization in strongly-interacting electronic systems. Then, I analyze heat transport properties of levitons in quantum Hall systems, which represent a new point of view on electron quantum optics, extending and generalizing the results obtained in the charge domain.
