Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology

TL;DR

This paper investigates the topological phases of a chiral p+ip superconductor with Dirac points, revealing conditions for higher-order and boundary-obstructed topological superconductivity using defect classification methods.

Contribution

It identifies the topological phases of a Dirac superconductor with specific symmetries and introduces an alternative defect classification approach for characterizing these phases.

Findings

Higher-order topological superconductor phase with C4 symmetry

Boundary-obstructed topological superconductor phase with C2 symmetry

Nested-Wilson loop fails as a topological invariant in this context

Abstract

We analyze the topological properties of a chiral ${p}+i{p}$ superconductor for a two-dimensional metal/semimetal with four Dirac points. Such a system has been proposed to realize second-order topological superconductivity and host corner Majorana modes. We show that with an additional $\mathsf{C}_4$ rotational symmetry, the system is in an intrinsic higher-order topological superconductor phase, and with a lower and more natural $\mathsf{C}_2$ symmetry, is in a boundary-obstructed topological superconductor phase. The boundary topological obstruction is protected by a bulk Wannier gap. However, we show that the well-known nested-Wilson loop is in general unquantized despite the particle-hole symmetry, and thus fails as a topological invariant. Instead, we show that the higher-order topology and boundary-obstructed topology can be characterized using an alternative defect classification approach, in which the corners of a finite sample is treated as a defect of a space-filling Hamiltonian. We establish "Dirac+$({p}+i{p})$" as a sufficient condition for second-order topological superconductivity.