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

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
C4 rotational symmetry, the system is in an intrinsic higher-order topological superconductor phase,
and with a lower C2 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.