A short course on topological insulators. Band structure and edge states in one and two dimensions

DOI10.1007/978-3-319-25607-8zbMath1331.82002arXiv1509.02295OpenAlexW3102897980MaRDI QIDQ2634840

János K. Asbóth, László Oroszlány, András Pályi

Publication date: 9 February 2016

Published in: Lecture Notes in Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.02295

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to statistical mechanics (82-02) Statistical mechanics of semiconductors (82D37) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Statistical mechanics of magnetic materials (82D40)

Related Items (47)

Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping ⋮ Detecting topological edge states with the dynamics of a qubit ⋮ Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence ⋮ Quadratic pseudospectrum for identifying localized states ⋮ Winding number statistics of a parametric chiral unitary random matrix ensemble* ⋮ Analytical solution of open crystalline linear 1D tight-binding models ⋮ Partition-based discrete-time quantum walks ⋮ Continuous topological transition from metal to dielectric ⋮ Topological insulating phase for anti-Hermitian Hamiltonians ⋮ Symmetry-resolved entanglement in a long-range free-fermion chain ⋮ Signatures of topological phase transitions in higher Landau levels of hgte/cdte quantum wells from an information theory perspective ⋮ Rigorous index theory for one-dimensional interacting topological insulators ⋮ Software implementation for calculating Chern and \(\mathbb{Z}_2\) topological invariants of crystalline solids with WIEN2k all-electron density functional package ⋮ Quantum Probing Topological Phase Transitions by Non‐Markovianity ⋮ Distinguishing the Topological Zero Mode and Tamm Mode in a Microwave Waveguide Array ⋮ Winding number statistics for chiral random matrices: Averaging ratios of parametric determinants in the orthogonal case ⋮ Edge States in 1D Rhombus Lattices ⋮ Tunable Mode Entanglement: Topological Su–Schrieffer–Heeger (SSH) Chain with an Embedded Aharonov–Bohm Quantum Ring ⋮ Non‐Hermitian Hartman Effect ⋮ On the Su–Schrieffer–Heeger model of electron transport: Low‐temperature optical conductivity by the Mellin transform ⋮ Topological plasmons in dimerized chains of nanoparticles: robustness against long-range quasistatic interactions and retardation effects ⋮ Eigenvalues and eigenfunctions of the perturbed non-Hermitian SSH Hamiltonian with PT symmetry ⋮ Symmetry-induced quasicrystalline waveguides ⋮ Particle and thermal transport through one dimensional topological systems via Lindblad formalism ⋮ Transmission from reverse reaction coordinate mappings ⋮ Dynamic defects in photonic Floquet topological insulators ⋮ Asymptotic Characterization of Localized Defect Modes: Su–Schrieffer–Heeger and Related Models ⋮ Scanning qubit probe of edge states in a topological insulator ⋮ On the ℤ2 topological invariant ⋮ Topological phenomena in honeycomb Floquet metamaterials ⋮ Various topological Mott insulators and topological bulk charge pumping in strongly-interacting boson system in one-dimensional superlattice ⋮ Topologically protected edge modes in one-dimensional chains of subwavelength resonators ⋮ An elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger model ⋮ Topological insulators and semimetals in classical magnetic systems ⋮ Scattering and quasilevels in the SSH model ⋮ Floquet spectrum and dynamics for non-Hermitian Floquet one-dimension lattice model ⋮ An elementary proof and detailed investigation of the bulk-boundary correspondence in the generic two-band model of Chern insulators ⋮ Topological properties of a class of Su-Schrieffer-Heeger variants ⋮ Asymptotic correlations in gapped and critical topological phases of 1D quantum systems ⋮ Entanglement in (4 + 1)-D-Dirac-type lattice model time-reversal-invariant ⋮ Topological Anderson insulators induced by random binary disorders ⋮ Nonlinear optical waveguide lattices: asymptotic analysis, solitons, and topological insulators ⋮ Gap sets for the spectra of regular graphs with minimum spectral gap ⋮ Topological transition in measurement-induced geometric phases ⋮ Qubits as Edge State Detectors: Illustration Using the SSH Model ⋮ The bulk-edge correspondence for continuous dislocated systems ⋮ Winding vectors of topological defects: multiband Chern numbers

This page was built for publication: A short course on topological insulators. Band structure and edge states in one and two dimensions