Self-consistent theory of current injection intodandd + issuperconductors

We present results for the steady-state nonlinear response of adx2-y2superconducting film connected to normal-metal reservoirs under voltage bias, allowing for a subdominants-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 pured-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 subdominants-wave pairing channel, it is in equilibrium energetically favorable for ans-wave order parameter componentΔsto appear near the interfaces in the time-reversal symmetry breaking combinationd + 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 thes-wave component to zero as the voltageeV→Δs. 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.