Self-consistent theory of current injection into d and d + is superconductors

Abstract

We present results for the steady-state nonlinear response of a superconducting film connected to normal-metal reservoirs under voltage bias, allowing for a subdominant s-wave component appearing near the interfaces. Our investigation is based on a current-conserving theory that self-consistently includes the non-equilibrium distribution functions, charge imbalance, and the voltage-dependencies of order parameters and scalar impurity self-energies. For a pure d-wave superconductor with [110] orientation of the interfaces to the contacts, the conductance contains a zero-bias peak reflecting the large density of zero-energy interface Andreev bound states. Including a subdominant s-wave pairing channel, it is in equilibrium energetically favorable for an s-wave order parameter component to appear near the interfaces in the time-reversal symmetry breaking combination d + is. The Andreev states then shift to finite energies in the density of states. Under voltage bias, we find that the non-equilibrium distribution in the contact area causes a rapid suppression of the s-wave component to zero as the voltage . The resulting spectral rearrangements and voltage-dependent scattering amplitudes lead to a pronounced non-thermally broadened split of the zero-bias conductance peak that is not seen in a non-selfconsistent Landauer–Büttiker scattering approach.