Emergence of a new symmetry class for Bogoliubov-de Gennes (BdG) Hamiltonians: Expanding ten-fold symmetry classes
arXiv:1810.07618 · doi:10.1080/01411594.2020.1723588
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.
Extensively revised version with a few new interpretations of calculations. Comments will be very much appreciated
References in corpus (9)
- Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
- Classification of topological quantum matter with symmetries
- Topological Crystalline Insulators
- Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
- The Helical Liquid and the Edge of Quantum Spin Hall Systems
- The space group classification of topological band insulators
- Exact ground states and topological order in interacting Kitaev/Majorana chains
- Topologically protected flat zero-energy surface bands in non-centrosymmetric superconductors
- Majorana Neutrino as Bogoliubov Quasiparticle