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

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 gives 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.