Nuclear magnetic relaxation rates of unconventional superconductivity in doped topological insulators

We study the temperature dependence of nuclear magnetic relaxation (NMR) rates to detect unconventional superconductivity in doped topological insulators, such as M(=Cu, Nb, Sr)(x) Bi2Se3 and Sn1-x In-x Te. The Hebel-Slichter coherence effect below a critical temperature T-c 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 He-3, the NMR rate has a conventional s-wave-like coherence peak below T-c. In contrast, in a fully-gapped isotropic topological superconducting state, this rate below T-c exhibits an antipeak profile. Moreover, in a twofold in-plane anisotropic topological superconducting state, there is no coherence effect, which is similar to that in a chiral p-wave state. We also claim in a model of CuxBi2Se3 that a signal of the fully-gapped odd-parity state is attainable from the change of the antipeak behavior depending on doping level. Thus, we reveal that the NMR rates shed light on unconventional superconductivity in doped topological insulators.