Odd-parity superconductors with two-component order parameters: nematic and chiral, full gap and Majorana node

TL;DR

This paper investigates odd-parity superconductors with two-component order parameters in trigonal and hexagonal systems, revealing nematic and chiral phases with distinct gap structures and Majorana fermions, inspired by experiments on Cu$_x$Bi$_2$Se$_3$.

Contribution

It introduces a theoretical framework for understanding nematic and chiral phases in odd-parity superconductors with strong spin-orbit coupling, highlighting their topological properties.

Findings

Nematic phase has a full gap, chiral phase has point nodes.

Chiral phase hosts Majorana fermions and surface arcs.

Two possible superconducting phases are identified below T_c.

Abstract

Motivated by the recent experiment indicating that superconductivity in the doped topological insulator Cu$_x$Bi$_2$Se$_3$ has an odd-parity pairing symmetry with rotational symmetry breaking, we study the general class of odd-parity superconductors with two-component order parameters in trigonal and hexagonal crystal systems. In the presence of strong spin-orbit interaction, we find two possible superconducting phases below $T_c$, a time-reversal-breaking (i.e., chiral) phase and an anisotropic (i.e., nematic) phase, and determine their relative energetics from the gap function in momentum space. The nematic superconductor generally has a full quasi-particle gap, whereas the chiral superconductor with a three-dimensional (3D) Fermi surface has point nodes with lifted spin degeneracy, resulting in itinerant Majorana fermions in the bulk and topological Majorana arcs on the surface.