Chiral $p-$wave superconductivity in Pb$_{1-x}$Sn$_{x}$Te: signatures from bound-state spectra and wavefunctions

Abstract

Surface superconductivity has recently been observed on the (001) surface of the topological crystalline insulator Pb 1−x Sn x Te using point-contact spectroscopy, and theoretically proposed to be of the chiral p−wave type. In this paper, we closely examine the conditions for realizing a robust chiral p−wave order in this system, rather than conventional s-wave superconductivity. Further, within the p-wave superconducting phase, we identify parameter regimes where impurity bound (Shiba) states depend crucially on the existence of the chiral p−wave order, and distinguish them from other regimes where the chiral p−wave order does exist but the impurity-induced subgap bound states cannot be used as evidence for it. Such a distinction can provide an easily realizable experimental test for chiral p−wave order in this system. Notably, we have obtained exact analytical expressions for the bound state wavefunctions in point defects, in the chiral p−wave superconducting state, and find that instead of the usual exponential decay profile that characterizes bound states, these states decay as a power-law at large distances from the defect. As a possible application of our findings, we also show that the zero-energy Shiba states in point defects possess an internal SU(2) rotational symmetry which enables them to be useful as quantum qubits.