Sea of Majorana fermions from pseudo-scalar superconducting order in three dimensional Dirac materials

We suggest that spin-singlet pseudo-scalar s-wave superconducting pairing creates a two dimensional sea of Majorana fermions on the surface of three dimensional Dirac superconductors (3DDS). This pseudo-scalar superconducting order parameter Delta(5), in competition with scalar Dirac mass m, leads to a topological phase transition due to band inversion. We find that a perfect Andreev-Klein reflection is guaranteed by presence of anomalous Andreev reflection along with the conventional one. This effect manifests itself in a resonant peak of the differential conductance. Furthermore, Josephson current of the Delta(5)|m|Delta(5) junction in the presence of anomalous Andreev reflection is fractional with 4 pi period. Our finding suggests another search area for condensed matter realization of Majorana fermions which are beyond the vortex-core of p-wave superconductors. The required Delta(5) pairing can be extrinsically induced by a conventional s-wave superconductor into a three dimensional Dirac material (3DDM).