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 $d+i{d}^{\prime }$-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 $d+i{d}^{\prime }$-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 $d+i{d}^{\prime }$-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.

10 pages, 6 figures

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• Impact of topology on the impurity effects in extended $s$-wave superconductors with spin-orbit coupling
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• Probing unconventional superconductivity in proximitized graphene by impurity scattering
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• Disorder and Zeeman coupling induced gap-filling states in the nodeless chiral superconducting Bi/Ni bilayer system
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• Chiral $p-$wave superconductivity in Pb${}_{1-x}$Sn${}_x$Te: signatures from bound-state spectra and wavefunctions