Emergence of a new symmetry class for Bogoliubov–de Gennes (BdG) Hamiltonians: expanding 10-fold symmetry classes

Abstract

ABSTRACTSymmetry plays an important role in the topological states of quantum matter. Cartan found three symmetry classes, Altland and Zirnbauer extended it to the 10-fold symmetry class for mesoscopic systems. We observe the 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 10-fold symmetry classes for topological states of quantum matter. These BdG Hamiltonians show many new, interesting and insightful results.