Non-equilibrium theory of tunneling into localized state in superconductor

A single static magnetic impurity in a fully-gapped superconductor leads to formation of an intragap quasiparticle bound state. At temperatures much below the superconducting transition, the energy relaxation and spin dephasing of the state are expected to be exponentially suppressed. The presence of such a state can be detected in electron tunneling experiments as a pair of conductance peaks at positive and negative biases. Here we show, that for an arbitrarily weak tunneling strength, the peaks have to be symmetric with respect to the applied bias. This is in contrast to the standard result that the tunneling conductance is proportional to the local (in general particle-hole asymmetric) density of states. The asymmetry can be recovered is one allows for either a finite density of impurity states, or that impurities are coupled to another, non-superconducting, equilibrium bath.