Quantum phase slips in the presence of finite-range disorder

To study the effect of disorder on quantum phase slips (QPS) in superconducting nanowires, we consider the plasmon-only model where disorder can be incorporated into a first-principles instanton calculation. We consider weak but general finite-range disorder and compute the formfactor in the QPS rate associated with momentum transfer. We find that the system maps onto dissipative quantum mechanics, with the dissipative coefficient controlled by the wave (plasmon) impedance $Z$ of the wire and with a superconductor-insulator transition at $Z_{\rm c}=6.5$ kOhm. The usual Ohmic resistivity of the wire at the transition point is non-universal. Its value depends on both the strength and the correlation length of disorder, and in the considered regime is much smaller than the normal-state resistivity. We argue that the system will remain in the same universality class after resistive effects at the QPS core are taken into account.