Universal conductivity at a 2d superconductor-insulator transition: the effects of quenched disorder and Coulomb interaction

We calculate the zero-temperature electrical conductivity at a superconductor-insulator transition in two spatial dimensions. We focus on transitions in the universality class of the dirty 3d XY model. We use a dual model consisting of a single Dirac fermion at zero density coupled to a Chern-Simons gauge field in the presence of a quenched random mass, with or without an unscreened Coulomb interaction. Our calculation is performed in a 1/Nf expansion, where Nf is the number of Dirac fermions.

At zeroth order, the model exhibits approximate particle-vortex self-dual electrical transport. Corrections of 1/Nf due to fluctuations in the Chern-Simons gauge field and disorder produce violations of self-duality. We find these violations would be supressed when the Coulomb interaction is present.