Protected boundary states in gapless topological phases

TL;DR

This paper classifies and analyzes protected boundary states in gapless topological phases like semimetals and nodal superconductors, revealing their topological origins and boundary manifestations.

Contribution

It provides a K-theory-based classification of stable Fermi surfaces and nodal lines, and explores the bulk-boundary correspondence in gapless topological phases.

Findings

Protected zero-energy boundary states can be linearly dispersing or flat bands.

Explicit surface spectra are computed for certain nodal superconductors.

Topological boundary states influence the surface density of states.

Abstract

We systematically study gapless topological phases of (semi-)metals and nodal superconductors described by Bloch and Bogoliubov-de Gennes Hamiltonians. Using K-theory, a classification of topologically stable Fermi surfaces in (semi-)metals and nodal lines in superconductors is derived. We discuss a generalized bulk-boundary correspondence that relates the topological features of the Fermi surfaces and superconducting nodal lines to the presence of protected zero-energy states at the boundary of the system. Depending on the case, the boundary states are either linearly dispersing (i.e., Dirac or Majorana states) or are dispersionless, forming two-dimensional surface flat bands or one-dimensional arc surface states. We study examples of gapless topological phases in symmetry class AIII and DIII, focusing in particular on nodal superconductors, such as nodal non-centrosymmetric superconductors. For some cases we explicitly compute the surface spectrum and examine the signatures of the topological boundary states in the surface density of states.