Nonequilibrium theory of tunneling into a localized state in a superconductor

A single static magnetic impurity in a fully gapped superconductor leads to the 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 in which the tunneling conductance is proportional to the local (in general, particle-hole asymmetric) density of states. The asymmetry can be recovered if one allows for either a finite density of impurity states, or if impurities are coupled to another, nonsuperconducting, equilibrium bath.

Figure 1

(a) Schematic representation of the problem: Electrons from an STM tip tunnel into a superconductor containing a single YSR state. (b) Effective representation after the particle-hole transformation on the spin-down tip electrons is performed. (c) Differential conductance of the system. The punctured line is the conductance of an “ideal” system, i.e., when the broadening is caused by the coupling to the STM tip only. The solid line accounts for the “extrinsic” broadening by an extra bath (other impurities or additional normal reservoir).