Odd-parity topological superconductor with nematic order: Application to Cu[subscript x] Bi[subscript 2] Se[subscript 3]

Abstract

Cu[subscript x] Bi[subscript 2] Se[subscript 3] was recently proposed as a promising candidate for time-reversal-invariant topological superconductors. In this work, we argue that the unusual anisotropy of the Knight shift observed by Zheng and co-workers (unpublished), taken together with specific heat measurements, provides strong support for an unconventional odd-parity pairing in the two-dimensional E[subscript u] representation of the D[subscript 3d] crystal point group, which spontaneously breaks the threefold rotational symmetry of the crystal, leading to a subsidiary nematic order. We predict that the spin-orbit interaction associated with hexagonal warping plays a crucial role in pinning the two-component order parameter and makes the superconducting state generically fully gapped, leading to a topological superconductor. Experimental signatures of the E[subscript u] pairing related to the nematic order are discussed.