Two-dimensional time-reversal-invariant topological insulators via Fredholm theory

DOI10.1007/s11040-020-09342-6OpenAlexW3104894399MaRDI QIDQ2007026

Yanyan Li

Publication date: 12 October 2020

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.00910

zbMATH Keywords

Fredholm theorytime-reversaltopological insulators\(Z_2\) invariants

Mathematics Subject Classification ID

(Semi-) Fredholm operators; index theories (47A53) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

Tight-binding reduction and topological equivalence in strong magnetic fields ⋮ Fredholm homotopies for strongly-disordered 2D insulators ⋮ The bulk-edge correspondence in three simple cases ⋮ On the Bott index of unitary matrices on a finite torus ⋮ Absolutely continuous edge spectrum of Hall insulators on the lattice

Cites Work

• Unnamed Item
• Unnamed Item
• Bulk and boundary invariants for complex topological insulators. From \(K\)-theory to physics
• \(\mathbb Z_{2}\)-indices and factorization properties of odd symmetric Fredholm operators
• Topological invariants of edge states for periodic two-dimensional models
• Bulk-edge correspondence for two-dimensional topological insulators
• Controlled topological phases and bulk-edge correspondence
• The \(K\)-theoretic bulk-edge correspondence for topological insulators
• Bulk-boundary correspondence for disordered free-fermion topological phases
• Topology and analysis. The Atiyah-Singer index formula and gauge- theoretic physics. Transl. from the German by D. D. Bleecker and A. Mader
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• Charge deficiency, charge transport and comparison of dimensions
• Topological boundary invariants for Floquet systems and quantum walks
• Bulk-edge correspondence for two-dimensional Floquet topological insulators
• The bulk-edge correspondence for disordered chiral chains
• Equality of bulk and edge Hall conductance revisited
• Classification of ``quaternionic Bloch-bundles: topological quantum systems of type AII
• Strongly disordered Floquet topological systems
• Dynamical delocalization in random Landau Hamiltonians
• Index theory for skew-adjoint Fredholm operators
• Equality of the bulk and edge Hall conductances in a mobility gap
• The ℤ2 index of disordered topological insulators with time reversal symmetry
• Differential geometric invariants for time-reversal symmetric Bloch-bundles: The “Real” case
• Periodic table for topological insulators and superconductors
• Characteristic Classes. (AM-76)
• Localization bounds for an electron gas
• The noncommutative geometry of the quantum Hall effect
• EDGE CURRENT CHANNELS AND CHERN NUMBERS IN THE INTEGER QUANTUM HALL EFFECT
• Chern number and edge states in the integer quantum Hall effect
• The Functional Calculus
• Chern numbers as half-signature of the spectral localizer
• The bulk-edge correspondence for continuous honeycomb lattices
• THE ANALYTIC CALCULATION OF THE INDEX OF ELLIPTIC EQUATIONS