Current fluctuations in unconventional superconductor junctions with impurity scattering

Abstract

The order parameter of bulk two-dimensional superconductors is classified as nodal if it vanishes for a direction in momentum space, or gapful if it does not. Each class can be topologically nontrivial if Andreev bound states are formed at the edges of the superconductor. Nonmagnetic impurities in the superconductor affect the formation of Andreev bound states and can drastically change the tunneling spectra for small voltages. Here, we investigate the mean current and its fluctuations for two-dimensional tunnel junctions between normal-metal and unconventional superconductors by solving the quasiclassical Eilenberger equation self-consistently, including the presence of nonmagnetic impurities in the superconductor. As the impurity strength increases, we find that superconductivity is suppressed for almost all order parameters since (i) at zero applied bias, the effective transferred charge calculated from the noise-current ratio tends to the electron charge e, and (ii) for finite bias, the current-voltage characteristics follows that of a normal-state junction. There are notable exceptions to this trend. First, gapful nontrivial (chiral) superconductors are very robust against impurity scattering due to the linear dispersion relation of their surface Andreev bound states. Second, for nodal nontrivial superconductors, only p(x)-wave pairing is almost immune to the presence of impurities due to the emergence of odd-frequency s-wave Cooper pairs near the interface. Due to their anisotropic dependence on the wave vector, impurity scattering is an effective pair-breaking mechanism for the remaining nodal superconductors. All these behaviors are neatly captured by the noise-current ratio, providing a useful guide to find experimental signatures for unconventional superconductivity.