Quantized Quadrupole Superconductors

Abstract

We introduce a class of superconductors termed "quantized quadrupole superconductors" that support Majorana corner modes according to the bulk-corner correspondence, distinct from previous works on the second-order topological superconductors. An intrinsic physical quantity for superconductors, i.e., the quadrupole moment serves as the topological invariant, which is always half-quantized due to the particle-hole symmetry. As examples, two types of mixed pairings, $d_{x^{2}-y^{2}}\pm id_{xy}$ and $d_{x^{2}-y^{2}}\pm is$, induced in the bilayer two-dimensional electron gases with Rashba spin-orbit coupling give the quadrupole phase. Extended discussions indicate that the nontrivial phase is robust against relative phase fluctuations in the mixed pairings and the disorders. Our schemes provide realistic platforms to implement Majorana zero modes, paving the way for studying the Majorana physics.