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

Abstract

We analyze the topological properties of a chiral $p+ip$ 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+$(p+ip)$" as a sufficient condition for second-order topological superconductivity.

11 pages, 6 figures

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• Controlling Majorana modes by $p$-wave pairing in two-dimensional $p+id$ topological superconductors
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