Emergence of a new symmetry class for Bogoliubov-de Gennes (BdG) Hamiltonians: Expanding ten-fold symmetry classes

TL;DR

This paper reports the discovery of a new symmetry class, called class X, for Bogoliubov-de Gennes Hamiltonians in spinful backgrounds, expanding the established ten-fold symmetry classification for topological quantum matter.

Contribution

It introduces a novel symmetry class for BdG Hamiltonians that extends the ten-fold classification, revealing new topological states and symmetry properties.

Findings

Emergence of a new symmetry class X for BdG Hamiltonians.

Absence of Kramers degeneracy in this new class.

Expansion of the ten-fold symmetry classification for topological states.

Abstract

Symmetry plays an important role in the topological states of quantum matter. Cartan found three symmetry classes, Altland and Zirnbauer extended it to the ten-fold symmetry class for mesoscopic systems. We observe emergence of a new symmetry class for BdG Hamiltonians. This new symmetry class appears for the BdG Hamiltonian in spinful background. We also observe the interesting feature that there is no evidence of Kramers's degeneracy for this BdG model Hamiltonian either in spinless or in spinful background. We call the extra symmetry class X, i.e, expanding the ten-fold symmetry classes for topological states of quantum matter. These BdG show many new, interesting and insightful results.