Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals

In the presence of certain symmetries, three-dimensional Dirac semimetals can\nharbor not only surface Fermi arcs, but also surface Dirac cones. Motivated by\nthe experimental observation of rotation-symmetry-protected Dirac semimetal\nstates in iron-based superconductors, we investigate the potential intrinsic\ntopological phases in a $C_{4z}$-rotational invariant superconducting Dirac\nsemimetal with $s_{\\pm}$-wave pairing. When the normal state harbors only\nsurface Fermi arcs on the side surfaces, we find that an interesting gapped\nsuperconducting state with a quartet of Bogoliubov-Dirac cones on each side\nsurface can be realized, even though the first-order topology of its bulk is\ntrivial. When the normal state simultaneously harbors surface Fermi arcs and\nsurface Dirac cones, we find that a second-order time-reversal invariant\ntopological superconductor with helical Majorana hinge states can be realized.\nThe criteria for these two distinct topological phases have a simple geometric\ninterpretation in terms of three characteristic surfaces in momentum space. By\nreducing the bulk material to a thin film normal to the axis of rotation\nsymmetry, we further find that a two-dimensional first-order time-reversal\ninvariant topological superconductor can be realized if the inversion symmetry\nis broken by applying a gate voltage. Our work reveals that diverse topological\nsuperconducting phases and types of Majorana modes can be realized in\nsuperconducting Dirac semimetals.\n