04483nmm a2200313 u 4500001001200000003002700012005001700039007002400056008004100080020002200121050001300143100002400156245012600180260007700306300001800383505183400401653003302235653002202268653003702290653003302327700002202360041001902382989003802401028002702439776002202466856008302488082001002571520158802581EB002176104EBX0100000000000000131388100000000000000.0cr|||||||||||||||||||||230926 ||| eng a978-1-4008-4673-3 4aQC611.951 aBernevig, B. Andrei00aTopological insulators and topological superconductorshElektronische RessourcecB. Andrei Bernevig with Taylor L. Hughes aPrinceton, New Jersey ; OxfordbPrinceton University Pressc2013, ©2013 aix, 247 pages0 aContents -- 1 Introduction -- 2 Berry Phase -- 2.1 General Formalism -- 2.2 Gauge-Independent Computation of the Berry Phase -- 2.3 Degeneracies and Level Crossing -- 2.3.1 Two-Level System Using the Berry Curvature -- 2.3.2 Two-Level System Using the Hamiltonian Approach -- 2.4 Spin in a Magnetic Field -- 2.5 Can the Berry Phase Be Measured? -- 2.6 Problems -- 3 Hall Conductance and Chern Numbers -- 3.1 Current Operators -- 3.1.1 Current Operators from the Continuity Equation -- 3.1.2 Current Operators from Peierls Substitution -- 3.2 Linear Response to an Applied External Electric Field -- 3.2.1 The Fluctuation Dissipation Theorem -- 3.2.2 Finite-Temperature Green's Function -- 3.3 Current-Current Correlation Function and Electrical Conductivity -- 3.4 Computing the Hall Conductance -- 3.4.1 Diagonalizing the Hamiltonian and the Flat-Band Basis -- 3.5 Alternative Form of the Hall Response -- 3.6 Chern Number as an Obstruction to Stokes' Theorem over the Whole BZ -- 3.7 Problems -- 4 Time-Reversal Symmetry -- 4.1 Time Reversal for Spinless Particles -- 4.1.1 Time Reversal in Crystals for Spinless Particles -- 4.1.2 Vanishing of Hall Conductance for T-Invariant Spinless Fermions -- 4.2 Time Reversal for Spinful Particles -- 4.3 Kramers' Theorem -- 4.4 Time-Reversal Symmetry in Crystals for Half-Integer Spin Par -- 4.5 Vanishing of Hall Conductance for T-Invariant Half-Integer Spin Particles -- 4.6 Problems -- 5 Magnetic Field on the Square Lattice -- 5.1 Hamiltonian and Lattice Translations -- 5.2 Diagonalization of the Hamiltonian of a 2-D Lattice in a Magnetic Field -- 5.2.1 Dependence on ky -- 5.2.2 Dirac Fermions in the Magnetic Field on the Lattice -- 5.3 Hall Conductance -- 5.3.1 Diophantine Equation and Streda Formula Method -- 5.4 Explicit Calculation of the Hall Conductance -- 5.5 Problems aEnergy-band theory of solids aSuperconductivity aSolid state physics--Mathematics aSuperconductors--Mathematics1 aHughes, Taylor L.07aeng2ISO 639-2 bGRUYMPGaDeGruyter MPG Collection50a110.1515/9781400846733 z978-0-691-15175-540uhttps://www.degruyter.com/document/doi/10.1515/9781400846733xVerlag3Volltext0 a530.43 aThis 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.