Axionic superconductivity in three dimensional doped narrow gap semiconductors

TL;DR

This paper explores a novel axionic superconducting state in doped narrow gap semiconductors, characterized by a $p+is$ pairing that breaks time-reversal and parity symmetries, leading to unique surface states and responses.

Contribution

It introduces the $p+is$ superconducting state as a dynamic axionic phase in doped semiconductors, highlighting its topological and symmetry-breaking properties.

Findings

Discovery of the $p+is$ state with simultaneous time-reversal and parity violation.

Presence of gapped Majorana surface states in the $p+is$ phase.

Anomalous surface thermal Hall effect and nontrivial $ heta$ vacuum responses.

Abstract

We consider the competition between the conventional s-wave and the triplet Balian-Werthamer or the B-phase pairings in the doped three dimensional narrow gap semiconductors, such as $\mathrm{Cu}_x\mathrm{Bi}_2\mathrm{Se}_3$ and $\mathrm{Sn}_{1-x}\mathrm{In}_x\mathrm{Te}$. When the coupling constants of the two contending channels are comparable, we find a simultaneously time-reversal and parity violating $p + is$ state at low temperatures, which provides an example of dynamic axionic state of matter. In contradistinction to the time-reversal invariant, topological B-phase, the $p + is$ state possesses gapped Majorana fermions as the surface Andreev bound states, which give rise to an anomalous surface thermal Hall effect. The anomalous gravitational and electrodynamic responses of the $p+is$ state can be described by the $\theta$ vacuum structure, where $\theta \neq 0$ or $\pi$.