Universal conductivity at a two-dimensional superconductor-insulator transition: The effects of quenched disorder and Coulomb interaction

We calculate the zero-temperature dc electrical conductivity in the collisionless ℏω/k_BT→∞ limit at superconductor-insulator transitions in the (2+1)d XY model universality class. We use a dual model consisting of a single Dirac fermion at zero density, coupled to a Chern-Simons gauge field and in the presence of a quenched random mass, with or without an unscreened Coulomb interaction. Our calculation is performed in a 1/N_f expansion, where N_f is the number of Dirac fermions. At the fixed point without Coulomb interaction, we obtain the universal conductivities (σₓₓ,σₓᵧ) = (0.97−0.52/N_f,−0.24+1.64/N_f)⋅(2e)²/h. At the fixed point with Coulomb interaction, we find (σₓₓ,σₓᵧ) = (0.97+1.09/Nf,−0.24+0.93N_f)⋅(2e)²/h. At zeroth order, the model exhibits particle-vortex self-dual electrical transport with σₓₓ ≲ (2e)²/h and small, but finite σₓᵧ. Corrections of O(1/N_f) due to fluctuations in the Chern-Simons gauge field and disorder produce violations of self-duality. These fluctuations reduce/enhance the longitudinal conductivity at the fixed point without/with the Coulomb interaction.