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arXiv · 2308.05155

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

Chao-Jung Lee·Michael Mulligan
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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.

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Chao-Jung Lee, Michael Mulligan. 2023-08-09. Universal conductivity at a 2d superconductor-insulator transition: the effects of quenched disorder and Coulomb interaction. https://doi.org/10.1103/physrevb.108.235142

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