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

• We construct a low-energy effective theory of topological s-wave pairing superconductors.
• Our approach is second-order perturbation with respect to the mass in the Dirac-type dispersion.
• The effective superconducting gap is a mixture of p- and s-wave-like components.
• The primary contribution is the p-wave component, but the s-wave part is not negligible in a massless limit.
• The effective theory is useful for understanding impurity effects in a topological superconductor.

We construct a low-energy effective theory of topological s  -wave pairing superconductors, focusing on the mean-field model of superconductor CuxBi2Se3CuxBi2Se3. 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 Bi2Se3Bi2Se3. 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 (Nagai et al., 2014) of the non-magnetic impurity effects.