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

Abstract

Recently, there is widespread interest in odd-parity (e.g., $p$-wave) superconductivity in strongly spin-orbit-coupled materials, such as doped topological insulators. Cu${}_{x}$Bi${}_{2}$Se${}_{3}$ is a prime example. A series of recent experiments, including NMR, specific heat, magnetoresistance, and torque magnetometry, has provided mounting evidence of odd-parity spin-triplet superconductivity in Cu${}_{x}$Bi${}_{2}$Se${}_{3}$ as well as Sr${}_{x}$Bi${}_{2}$Se${}_{3}$ and Nb${}_{x}$Bi${}_{2}$Se${}_{3}$. Here, the authors construct a general theory of such degenerate superconducting components and the competition between chiral and nematic states. They derive a general criterion to establish which state is energetically favored, which highlights the crucial role of spin-orbit coupling. In particular, when applied to the specific case of Cu${}_{x}$Bi${}_{2}$Se${}_{3}$, the theory is consistent with three key experimental findings: a full pairing gap, triplet pairing, and spontaneous rotational symmetry breaking. Remarkably, both nematic and chiral superconductors with odd-parity pairing symmetry are topological superconductors, belonging respectively to time-reversal-invariant (class DIII) and time-reversal-breaking (class D) categories of the topological classification. The authors show that due to the nonunitary nature of chiral pairing in spin-orbit coupled materials, spin nondegenerate point nodes realize Majorana fermion quasiparticles in three dimensions.