Theory of low-energy behaviors in topological s-wave pairing superconductors

We construct a low-energy effective theory of topological s-wave pairing superconductors, focusing on the mean-field model of superconductor mbox{Cu}_xmbox{Bi}₂mbox{Se}₃. Our approach is second-order perturbation with respect to the inverse of the mass (i.e., large-mass expansion) in the Dirac-type electron dispersion from topological insulator mbox{Bi}₂mbox{Se}₃. Since the Dirac-type dispersion with a large mass describes non-relativistic electrons, the large-mass expansion corresponds to a low-energy theory with respect to the original setup. We show that the effective gap function has not only a p-wave-like component as the primary contribution, but also an s-wave-like one as higher-order corrections. The mixture of p- and s-wave explains the numerical results [Phys. Rev. B 89 (2014) 214506] of the non-magnetic impurity effects.