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

TL;DR

This paper explores various topological superconducting phases and Majorana modes in superconducting Dirac semimetals with specific symmetries, revealing new surface states and hinge modes driven by the material's surface and symmetry properties.

Contribution

It identifies novel topological phases, including surface Bogoliubov-Dirac cones and helical Majorana hinge modes, in superconducting Dirac semimetals with $C_{4z}$ symmetry.

Findings

Gapped superconducting state with Bogoliubov-Dirac cones on side surfaces.

Second-order topological superconductor with Majorana hinge states.

Realization of 2D topological superconductor by symmetry breaking via gating.

Abstract

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