Time-reversal and rotation symmetry breaking superconductivity in Dirac materials

TL;DR

This paper explores how mixed symmetry superconducting phases in Dirac materials can break time-reversal symmetry due to magnetic dopants, leading to novel phases with unique quasiparticle excitations and surface states.

Contribution

It demonstrates that coupling between order parameters and magnetic dopants induces TRSB phases with complex quasiparticle spectra and surface states, expanding understanding of superconductivity in Dirac materials.

Findings

Identification of TRSB phases with Weyl nodes and nodal lines

Magnetic dopants induce rotation symmetry breaking

Consistent with experiments on Nb$_x$Bi$_2$Se$_3$

Abstract

We consider mixed symmetry superconducting phases in Dirac materials in the odd parity channel, where pseudoscalar and vector order parameters can coexist due to their similar critical temperatures when attractive interactions are of finite range. We show that the coupling of these order parameters to unordered magnetic dopants favors the condensation of novel time-reversal symmetry breaking (TRSB) phases, characterized by a condensate magnetization, rotation symmetry breaking, and simultaneous ordering of the dopant moments. We find a rich phase diagram of mixed TRSB phases characterized by peculiar bulk quasiparticles, with Weyl nodes and nodal lines, and distinctive surface states. These findings are consistent with recent experiments on Nb$_x$Bi$_2$Se$_3$ that report evidence of point nodes, nematicity, and TRSB superconductivity induced by Nb magnetic moments.