Higher-order topological superconductivity: possible realization in Fermi gases and Sr₂RuO₄

We propose to realize second-order topological superconductivity in bilayer spin-polarized Fermi gas superfluids. We focus on systems with intralayer chiral p-wave pairing and with tunable interlayer hopping and interlayer interactions. Under appropriate circumstance, an interlayer even-parity s- or d-wave pairing may coexist with the intralayer p-wave. Such mixed-parity phases do not carry one-dimensional gapless Majorana modes on the boundary, but could support Majorana zero modes at the corners of the system geometry, the end points of superconducting domain walls, as well as certain bulk defects. We show how the number and location of the Majorana zero modes can be tuned by the interlayer pairing and hopping. Generalized to spinful systems, we further propose that the putative p-wave superconductor Sr₂RuO₄, when placed under uniaxial strains, may also realize the desired topological phase.