Quantum Phase Slips in the Presence of Finite-Range Disorder

To study the effect of disorder on quantum phase slips (QPSs) in superconducting wires, 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 form factor 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 $Z=6.5\mathrm{k}\Omega$. We speculate that the system will remain in this universality class after resistive effects at the QPS core are taken into account.