Topological quantum phase transitions in the spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings

TL;DR

This paper explores the topological phases of a spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings, revealing conditions for Majorana fermions and flat bands through symmetry analysis and topological invariants.

Contribution

It identifies multiple topological invariants in the BdG Hamiltonian and characterizes the emergence of Majorana fermions and flat bands in this specific superconductor system.

Findings

Edge spectrum exhibits Dirac cones or flat bands.

Majorana flat bands require higher symmetry for stability.

Pfaffian invariant and winding number determine flat band locations.

Abstract

We examine the topological properties of a spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings. We demonstrate that there are several topological invariants in the Bogoliubov-de Gennes (BdG) Hamiltonian by symmetry analysis. We use the Pfaffian invariant $\mathcal{P}$ for the particle-hole symmetry to demonstrate all the possible phase diagrams of the BdG Hamiltonian. We find that the edge spectrum is either Dirac cone or flat band which supports the emergence of the Majorana fermion in this system. For the Majorana flat bands, a higher symmetric BdG Hamiltonian is needed to make them topologically stable. The Pfaffian invariant $\mathcal{P}(k_{y})$ and the winding number $\mathcal{W}(k_{y})$ are used in determining the location of the Majorana flat bands.