Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory

Abstract

We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant, define a new one for the edge, and show their equivalence (the bulk-edge correspondence) via homotopy.

arXiv comment18 pages

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Cited by in corpus (4)

• On the Bott index of unitary matrices on a finite torus
• Fredholm Homotopies for Strongly-Disordered 2D Insulators
• Absolutely continuous edge spectrum of topological insulators with an odd time-reversal symmetry
• Absolutely Continuous Edge Spectrum of Hall Insulators on the Lattice