Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians

TL;DR

This paper introduces a comprehensive method for constructing symmetry-based topological invariants for superconducting systems using Bogoliubov-de Gennes Hamiltonians, enabling systematic topological classification from high-symmetry point data.

Contribution

It generalizes existing symmetry-based indicators to superconducting Hamiltonians, providing a complete set of invariants for topological classification.

Findings

Constructed symmetry-based topological invariants for superconductors.

Provided a systematic method to compute invariants from high-symmetry points.

Extended previous indicators to Bogoliubov-de Gennes Hamiltonians.

Abstract

We develop a systematic approach for constructing symmetry-based indicators of a topological classification for superconducting systems. The topological invariants constructed in this work form a complete set of symmetry-based indicators that can be computed from knowledge of the Bogoliubov-de Gennes Hamiltonian on high-symmetry points in Brillouin zone. After excluding topological invariants corresponding to the phases without boundary signatures, we arrive at natural generalization of symmetry-based indicators [H. C. Po, A. Vishwanath, and H. Watanabe, Nature Comm. 8, 50 (2017)] to Hamiltonians of Bogoliubov-de Gennes type.