Impurity bound states in fully gapped \(d\)-wave superconductors with subdominant order parameters

Abstract

Impurities in superconductors and their induced bound states are important both for engineering novel states such as Majorana zero-energy modes and for probing bulk properties of the superconducting state. The high-temperature cuprates offer a clear advantage in a much larger superconducting order parameter, but the nodal energy spectrum of a pure \(d\)-wave superconductor only allows virtual bound states. Fully gapped \(d\)-wave superconducting states have however been proposed in several cuprate systems thanks to subdominant order parameters producing \(d+is\)- or \(d+id'\)-wave superconducting states. Here we study both magnetic and potential impurities in these fully gapped \(d\)-wave superconductors. Using analytical T-matrix and complementary numerical tight-binding lattice calculations, we show that magnetic and potential impurities behave fundamentally different in \(d+is\)- and \(d+id'\)-wave superconductors. In a \(d+is\)-wave superconductor, there are no bound states for potential impurities, while a magnetic impurity produces one pair of bound states, with a zero-energy level crossing at a finite scattering strength. On the other hand, a \(d+id'\)-wave symmetry always give rise to two pairs of bound states and only produce a reachable zero-energy level crossing if the normal state has a strong particle-hole asymmetry.