“Universal conductance” at a percolative superconductor-insulator transition in two dimensions

Precisely at the percolation threshold, we show that a superconductor-insulator composite in 2d behaves like a normal metal, with a conductance ge which is a universal function of the material parameters. For a composite of BCS superconductor and insulator, we find that g̃e = C(g̃Dg̃nεI)12, where εI is the dielectric constant of the insulating component, g̃D = Δd/e2, Δ is the BCS energy gap, d is the film thickness, and C is a dimensionless constant of order unity. g̃e and g̃n are the conductances of the film at threshold, and of the normal component, both measured in units of e2/ħ. Very near the threshold, g̃e falls to zero below a gap which vanishes at pc according to the power law |p − pc|s + t)/2, where s and t are the standard percolation exponents. Above but not below pc, the composite exhibits a perfect-conductance delta-function whose strength falls to zero as (p − pc)t.