Scattering theory of topological insulators and superconductors

By I. C. Fulga, F. Hassler, A. Akhmerov. 2011

146 citations recorded by the source corpus.

The topological invariant of a topological insulator (or superconductor) is given by the number of symmetry-protected edge states present at the Fermi level. Despite this fact, established expressions for the topological invariant require knowledge of all states below the Fermi energy. Here, we propose a way to calculate the topological invariant employing solely its scattering matrix at the Fermi level without knowledge of the full spectrum. Since the approach based on scattering matrices requires much less information than the Hamiltonian-based approaches (surface versus bulk), it is numerically more efficient. In particular, is better-suited for studying disordered systems. Moreover, it directly connects the topological invariant to transport properties potentially providing a new way to probe topological phases.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/6afb6350f4049c41cd5a61dfd263bdaafd08fd81

Citations in the corpus

• A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions (2015, unknown): “at is hard to construct [31], which makes the invariant difficult to calculate. An altogether different approach, which is robust and calculatable, uses the scattering matrix instead of the Hamiltonian[13]. In this Chapter we review a definition of the bulk Z 2 invariant[37] based on the dimensional r”