Second-order Dirac superconductors and magnetic field induced Majorana hinge modes

Understand

We identify three-dimensional higher-order superconductors characterized by the coexistence of one-dimensional Majorana hinge states and gapless surface sates.

• We show how such superconductors can be obtained starting from the model of a spinful quadrupolar semimetal with two orbitals and adding an s-wave superconducting pairing term.
• By considering all the possible s-wave pairings satisfying Fermi-Dirac statistics we obtain six different superconducting models.
• We find that for two of these models a flat-band of hinge Majorana states coexist with surface states, and that these models have a non-vanishing quadrupole-like topological invariant.