  Higher-order topological phases are gapped phases of matter that host gapless
corner or hinge modes. For the case of superconductors, corner or hinge modes
are gapless Majorana modes or Majorana zero modes. To construct 3d higher-order
topological superconductors, we consider a topological-insulator/superconductor
multilayer under in-plane Zeeman coupling. We found three different types of
higher-order topological superconductor phases, a second-order topological
superconductor phase with Majorana hinge flat bands, a second-order Dirac
superconductor phase with surface Majorana cones and Majorana hinge arcs, and
nodal-line superconductor phases with drumhead surface states and Majorana
hinge arcs.

Superconductivity