Superconducting higher-order semimetals : Second-order Dirac superconductors and magnetic field induced higher-order topological superconductivity

We identify three dimensional superconductors that exhibit various forms of higher order topology. We show how such superconductors can be obtained through superconducting instabilities induced in higher order quadrupole topological semimetals [1]. In our models the normal-state degrees of freedom consist of two orbitals and spin in an electronic structure that forms a quadrupolar topological semimetal. We consider all possible s-wave superconducting pairing terms satisfying Fermi-Dirac statistics and obtain six different superconducting models. We find that four of the models have a non-zero residual quadrupole-like topology, and therefore topologically protected Majorana hinge states on the four hinges of the sample. The other two models have no quadrupolar topology yet, in the presence of an external magnetic field, exhibit helical hinge states localized at only two of the four hinges. For these two models we also find that the pair of corners exhibiting hinge states switches upon a change of sign of the magnetic field.

[1]. M. Lin, T.L. Hughes, arXiv:1708.08457.