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.