Bulk and boundary invariants for complex topological insulators. From \(K\)-theory to physics

From MaRDI portal
Publication:256930

DOI10.1007/978-3-319-29351-6zbMath1342.82002arXiv1510.08744OpenAlexW3101118761MaRDI QIDQ256930

Hermann Schulz-Baldes, Emil Prodan

Publication date: 11 March 2016

Published in: Mathematical Physics Studies (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.08744




Related Items (only showing first 100 items - show all)

A \(\mathbb{Z}_2\)-topological index for quasi-free fermionsBeyond Diophantine Wannier diagrams: gap labelling for Bloch-Landau HamiltoniansThe index theorem of lattice Wilson-Dirac operators via higher index theoryWinding number statistics of a parametric chiral unitary random matrix ensemble*Locally equivalent quasifree states and index theoryT-duality simplifies bulk-boundary correspondence: the noncommutative caseTopology of Fermi surfaces and anomaly inflowsNotes on topological insulatorsGeneralized Connes–Chern characters inKK-theory with an application to weak invariants of topological insulatorsTight-binding reduction and topological equivalence in strong magnetic fieldsTopological insulators from the perspective of non-commutative geometry and index theoryA groupoid approach to interacting fermionsUnnamed ItemUniversal edge transport in interacting Hall systemsTopological boundary invariants for Floquet systems and quantum walksChern numbers, localisation and the bulk-edge correspondence for continuous models of topological phasesUbiquity of conical points in topological insulatorsTopology in shallow-water waves: a violation of bulk-edge correspondenceA many-body index for quantum charge transportFu-Kane-Mele monopoles in semimetalsThe tenfold way redux: Fermionic systems with \(N\)-body interactionsNon-commutative Chern numbers for generic aperiodic discrete systemsTopological invariants for interface modesCyclic cohomology for graded \(C^{\ast,r}\)-algebras and its pairings with van Daele \(K\)-theoryThe cohomology invariant for class DIII topological insulatorsEfficient computation of theW3topological invariant and application to Floquet–Bloch systemsLocal disorder, topological ground state degeneracy and entanglement entropy, and discrete anyonsIndex theory and topological phases of aperiodic latticesTopology in shallow-water waves: a spectral flow perspectiveCrystallographic T-dualityBulk-edge correspondence and the cobordism invariance of the indexEquivalence of electric, magnetic, and electromagnetic Chern numbers for topological photonic crystalsEdge-following topological statesThe topological classification of one-dimensional symmetric quantum walksWannier functions and ℤ2 invariants in time-reversal symmetric topological insulatorsAn elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger modelApproximate symmetries and conservation laws in topological insulators and associated \(\mathbb{Z}\)-invariantsGlobal topology of Weyl semimetals and Fermi arcsSpectral Flow Argument Localizing an Odd Index PairingThe Cayley transform in complex, real and graded K-theoryGood Wannier bases in Hilbert modules associated to topological insulatorsChiral Floquet systems and quantum walks at half-periodDimensional reduction and scattering formulation for even topological invariantsThe topology of mobility-gapped insulatorsOperators, Algebras and Their Invariants for Aperiodic TilingsSpectral structures and topological methods in mathematical quasicrystals. Abstracts from the workshop held October 1--7, 2017Spectral flow for skew-adjoint Fredholm operatorsEdge states in ordinary differential equations for dislocationsSome remarks on $\mathrm{K}_0$ of noncommutative toriQuantization of edge currents along magnetic interfaces: a \(K\)-theory approachTopological edge states for disordered bosonic systemsThe noncommutative index theorem and the periodic table for disordered topological insulators and superconductorsThe spectral localizer for semifinite spectral triplesCoarse geometry and topological phasesCrystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indicesOn ℤ2-indices for ground states of fermionic chainsRational indices for quantum ground state sectorsTopological insulators and the Kane–Mele invariant: Obstruction and localization theorySkew localizer and \(\mathbb{Z}_2\)-flows for real index pairingsThe non-commutative topology of two-dimensional dirty superconductorsToeplitz Extensions in Noncommutative Topology and Mathematical PhysicsT-duality and the bulk-boundary correspondenceBulk-edge correspondence for two-dimensional Floquet topological insulatorsControlled topological phases and bulk-edge correspondenceBraiding flux-tubes in topological quantum and classical lattice models from class-DClassification of topological invariants related to corner statesThe \(K\)-theoretic bulk-boundary principle for dynamically patterned resonatorsThe \(K\)-theoretic bulk-edge correspondence for topological insulatorsTwo-dimensional time-reversal-invariant topological insulators via Fredholm theoryThe noncommutative geometry of the Landau Hamiltonian: metric aspectsT-duality simplifies bulk-boundary correspondence: some higher dimensional casesOn spectral flow and Fermi arcsChiral vector bundlesThe bulk-edge correspondence for disordered chiral chainsThe Schrödinger formalism of electromagnetism and other classical waves -- how to make quantum-wave analogies rigorousTopological invariants and corner states for Hamiltonians on a three-dimensional latticeA non-commutative framework for topological insulatorsAn elementary proof and detailed investigation of the bulk-boundary correspondence in the generic two-band model of Chern insulatorsEigenvalue crossings in Floquet topological systems`Real' Gerbes and Dirac cones of topological insulatorsThe bulk-edge correspondence in three simple casesAlmost commuting self-adjoint matrices: The real and self-dual casesPseudodifferential calculus on noncommutative tori, I. Oscillating integralsChern numbers as half-signature of the spectral localizerContinuous bulk and interface description of topological insulatorsBulk spectrum and K-theory for infinite-area topological quasicrystalsQuantum walks: Schur functions meet symmetry protected topological phasesThe bulk-edge correspondence for continuous honeycomb latticesSpectral flow of monopole insertion in topological insulatorsDefect modes for dislocated periodic mediaBulk-boundary correspondence for disordered free-fermion topological phasesToeplitz operators on concave corners and topologically protected corner statesSpectral flows of Toeplitz operators and bulk-edge correspondenceThe spectral localizer for even index pairingsParticle–hole symmetries in condensed matterComputing Edge States without Hard TruncationOn the Bott index of unitary matrices on a finite torusDixmier trace formulas and negative eigenvalues of Schrödinger operators on curved noncommutative toriThe bulk-edge correspondence for continuous dislocated systemsAbsolutely continuous edge spectrum of Hall insulators on the lattice




This page was built for publication: Bulk and boundary invariants for complex topological insulators. From \(K\)-theory to physics