Comparing topological edge state characteristics of chiral topological phases between theory and experiment

A defining characteristic of nontrivial topological electronic phases is the existence of gapless states on the edge or boundary, the so-called topological edge states. The presence of edge states can therefore serve as a means to identify topological phases in experiment. To enable and facilitate quantitative connections to experiments, in particular electron tunneling experiments, in this talk we present an extensive and detailed characterization of experimentally accessible edge state properties for a class of chiral topological phases, focusing in particular on chiral superconductors. We obtain exact solutions for the edge state wave function and energy dispersion in representative two-band tight-binding models with open boundary conditions, and show how important characteristics such as decay length and local density of states (LDOS) depend on quasiparticle band structure parameters. We further demonstrate that multiple approximation methods can provide excellent descriptions of these characteristics, which can be exploited when the lattice model tight-binding description becomes complicated. We apply our theory to the recently discovered superconducting system Sn/Si(111), for which signatures of fully gapped chiral pairing have been reported. We finally show how our results can be straightforwardly extended to more general topological phases, such as topological crystalline insulators and three-dimensional topological semimetals.