Nuclear magnetic relaxation rates of unconventional superconductivity in doped topological insulators

TL;DR

This paper investigates how nuclear magnetic relaxation rates can reveal signatures of unconventional topological superconductivity in doped topological insulators, distinguishing different pairing states through their unique NMR signatures.

Contribution

It provides a theoretical analysis linking NMR rate behaviors to various topological superconducting states in doped topological insulators, aiding experimental identification.

Findings

NMR rates show a coherence peak in nodal topological states.

Fully-gapped isotropic states exhibit an anti-peak below Tc.

No coherence effect in in-plane anisotropic topological states.

Abstract

We study the temperature dependence of nuclear magnetic relaxation (NMR) rates to detect a sign of topological superconductivity in doped topological insulators, such as $M$($=$Cu,Nb,Sr)$_{x}$Bi$_{2}$Se$_{3}$ and Sn$_{1-x}$In$_{x}$Te. The Hebel-Slichter coherence effect below a critical temperature Tc depends on the superconducting states predicted by a minimal model of doped topological insulators. In a nodal anisotropic topological state similar to the ABM-phase in $^{3}$He, the NMR rate has a conventional $s$-wave like coherence peak below Tc. In contrast, in a fully-gapped isotropic topological superconducting state, this rate below Tc exhibits an anti-peak profile. Moreover, in a two-fold in-plane anisotropic topological superconducting state, there is no coherence effect, which is similar to that in a chiral $p$-wave state. Thus, we reveal that the NMR rates shed light on unconventional superconductivity in doped topological insulators.