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

Abstract

We calculate the zero-temperature dc electrical conductivity in the collisionless ℏω/kBT→∞ 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/Nf expansion, where Nf is the number of Dirac fermions. At the fixed point without Coulomb interaction, we obtain the universal conductivities (σxx,σxy)=(0.97−0.52/Nf,−0.24+1.64/Nf)·(2e)2/h. At the fixed point with Coulomb interaction, we find (σxx,σxy)=(0.97+1.09/Nf,−0.24+0.93Nf)·(2e)2/h. At zeroth order, the model exhibits particle-vortex self-dual electrical transport with σxx≲(2e)2/h and small, but finite σxy. Corrections of O(1/Nf) 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.

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