Second-order Topological Superconductors

Abstract

Topological superconductors are fully gapped in the bulk but host Majorana modes on their boundaries. We extend this notion to a new class of superconductors, second-order topological superconductors, that host Majorana modes instead on second-order boundaries, i.e., corners of a two-dimensional system and hinges for a three-dimensional system. Here we propose two general scenarios in which second-order topological superconductivity can be realized. First, we show that $p_x+ip_y$-wave pairing in a (doped) Dirac semimetal in two dimensions with four mirror symmetric Dirac nodes realizes second-order topological superconductivity. Second, we show that the four Dirac nodes can also come from the BdG spectrum of a $d$-wave superconductor. In this scenario, with an additional $p$-wave pairing that gaps out the Dirac nodes, the system realizes second-order topological superconductivity as well. We show that these exotic superconducting states can be intrinsically realized in a metallic system with electronic interactions, or induced by proximity effect.