Andreev spectroscopy and surface density of states for a three-dimensional time-reversal-invariant topological superconductor

A topological superconductor is a fully gapped superconductor that exhibits exotic zero-energy Andreev surface states at interfaces with a normal metal. In this paper we investigate the properties of a three-dimensional time-reversal invariant topological superconductor by means of a two-band model with unconventional pairing in both the interband and intraband channels. Due to the bulk-boundary correspondence the presence of Andreev surface states in this system is directly related to the topological structure of the bulk wave functions, which is characterized by a winding number. Using quasiclassical scattering theory we construct the spectrum of the Andreev bound states that appear near the surface and compute the surface density of states for various surface orientations. Furthermore, we consider the effects of band splitting, i.e., the breaking of an inversion-type symmetry, and demonstrate that in the absence of band splitting there is a direct transition between the fully gapped topologically trivial phase and the nontrivial phase whereas in the presence of band splitting there exists a finite region of a gapless nodal superconducting phase between the fully gapped topologically trivial and nontrivial phases.