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

TL;DR

This paper demonstrates that pseudo-scalar superconducting order in three-dimensional Dirac materials can host Majorana fermions, revealing new topological phases with distinctive transport signatures and Josephson effects.

Contribution

It introduces the concept that pseudo-scalar pairing induces Majorana fermions in 3D Dirac superconductors, expanding the understanding of topological superconductivity.

Findings

Pseudo-scalar order parameter causes gap closing and reopening.

Presence of a two-dimensional Majorana sea at the gap kink.

Observation of a 4π periodic Josephson effect.

Abstract

We find that singlet superconducting pairing can lead to Majorana fermions in three dimensional Dirac superconductors (3DDS) if the pairing order parameter is a pseudo-scalar, i.e. it changes sign under mirror reflection. The pseudo-scalar superconducting order parameter, $\Delta_5$ can close and reopen the spectral gap caused by the scalar Dirac mass $m$ in a three-dimensional Dirac material (3DDM), giving rise to a two-dimensional Majorana sea (2DMS) at the plane of the gap kink. By bringing the Hamiltonian into a canonical form which then gives the winding number, we show that this system belongs to the DIII class of topological superconductors. We calculate the transport signature of 2DMS, namely a perfect Andreev-Klein transmission that manifests in a robust peak in the differential conductance. Further, we find the $4\pi$ periodicity in the $\Delta_5|m|\Delta_5$ Josephson junc- tions. Gauge transformed version of the present scenario implies that the interface of a conventional s-wave superconductor with a peculiar 3DDM whose mass is a pseudo-scalar, m5 also hosts a 2DMS.