Inverse coherence effects in nuclear magnetic relaxation rates as a sign of topological superconductivity

TL;DR

This paper proposes that the temperature dependence of nuclear magnetic relaxation rates can serve as a bulk signature of three-dimensional topological superconductivity, showing an inverse coherence effect distinct from conventional superconductors.

Contribution

It introduces the inverse coherence effect in NMR rates as a bulk indicator of topological superconductivity and demonstrates this through self-consistent calculations for Cu$_{x}$Bi$_{2}$Se$_{3}$.

Findings

Inverse coherence effect causes an anti-peak in NMR rates below T_c.

The effect results from a twist in order parameters related to orbital and spin degrees.

The NMR rate shows a concave temperature dependence in the topological state.

Abstract

We reveal that three-dimensional multi-orbital topological superconductivity can be identified by a bulk measurement, i.e., the temperature dependence of nuclear magnetic relaxation (NMR) rates. Below a critical temperature $T_{\rm c}$, the NMR rate in the topological state exhibits an anti-peak profile, which is opposite to the conventional $s$-wave state. This inversion coherence effect comes from a twist of order parameters with respect to orbital and spin degrees of freedom. Our self-consistent calculations in the model for Cu$_{x}$Bi$_{2}$Se$_{3}$ prove that the inverse coherence effect appears as a concave temperature dependence of the NMR rates. We propose that a time-reversal-invariant orbital-singlet spin-triplet topological superconductivity is characterized by the temperature dependence of the NMR rate.