Erratum: Tuning a Josephson junction through a quantum critical point

We have corrected a problem in our computational code that determined the normal-state resistance. In general, we find a reduction of Rn when the correlations are large and there is more than one plane in the barrier. The reduction of Rn affects four figures from the original paper, and affects the conjecture about ‘‘intrinsic pinholes.’’ We discovered that our calculations had not fully converged for the interacting density of states and self energy for small frequencies. This created numerical errors in the calculation of the resistance via the Kubo formula. The error has now been corrected and all resistances recalculated. The error does not affect the superconducting properties at all since they were calculated with a different imaginary-axis code. We show a corrected plot of the Josephson critical current, the normal-state resistance Rn , and the characteristic voltage IcRn for the single plane and two-plane barriers. The plots are on a semilogarithmic scale. The main difference is in the characteristic voltage IcRn in Fig. 4~c!. The optimization now occurs at the ballistic metal limit of U→0, where the IcRn product approaches the product of the bulk critical current times the Sharvin resistance, which is 0.287t/e 51.45D/e . As UFK increases, the characteristic voltage decreases and becomes flat as expected by the AmbegaokarBaratoff limit. The results for the two-plane barrier are modified significantly. The reduction of IcRn is more dramatic for moderate scattering, and as we move into an insulating barrier, we also reproduce the Ambegaokar-Baratoff result, and the unphysical increase with UFK has disappeared. Next we show the corrected figure for the moderately thick barrier ~with Nb55). The critical current, normal-state resistance, and characteristic voltage are plotted in Fig. 9 for Nb55 ~diamond!. The characteristic voltage has interesting behavior. Starting at a value about 20% less than the Ambegaokar-Baratoff limit in the metallic regime, the voltage initially decreases with correlation strength, then has a rapid increase starting at the metal-insulator transition, reaching a maximum near the Ambegaokar-Baratoff result ~up to the values of UFK that we can safely determine the IcRn product!. Junctions in this correlated regime do see an enhancement of the characteristic voltage on the insulating side of the metal-insulator transition, but the enhancement is at most only 20–30 % higher than in the thin tunnel junctions. The thick barrier junction Nb520 has the most significant corrections. We find that the calculations become untrustworthy when UFK becomes too large. We show results up to UFK56, but it is possible the IcRn product is too large there, due to an overestimate of the critical current Ic , as can be inferred by the slight upturn in the Ic data in panel ~a!.