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

Abstract

We calculate the zero-temperature universal 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 $1/N_f$ expansion, where $N_f$ is the number of Dirac fermions. At zeroth order, the model exhibits particle-vortex self-dual electrical transport with ${\sigma }_{xx}\lesssim (2e{)}^2/h$ and small, but finite ${\sigma }_{xy}$. Corrections of $\mathcal{O}(1/N_f)$ due to fluctuations in the Chern-Simons gauge field and disorder produce violations of self-duality. We find these violations to be milder when the Coulomb interaction is present.

16 pages + three appendices, 8 figures

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• Graphene via large N I: Renormalization
• Gifts from anomalies: Exact results for Landau phase transitions in metals
• Loop current fluctuations and quantum critical transport
• Quantum critical behavior of the superfluid-Mott glass transition

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