Sharp superconductor-insulator transition in short wires

Recent experiments on short MoGe nanowires show a sharp superconductor-insulator transition tuned by the normal state resistance of the wire, with a critical resistance of R_c ≈ R_Q = h/(4e²). These results are at odds with a broad range of theoretical work on Josephson-like systems that predicts a smooth transition, tuned by the value of the resistance that shunts the junction. We develop a self-consistent renormalization group treatment of interacting phase-slips and their dual counterparts, correlated cooper pair tunneling, beyond the dilute approximation. This analysis leads to a very sharp transition with a critical resistance of R_Q. The addition of the quasi-particles' resistance at finite temperature leads to a quantitative agreement with the experimental results. This self-consistent renormalization group method should also be applicable to other physical systems that can be mapped onto similar sine-Gordon models, in the previously inaccessible intermediate-coupling regime.