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

TL;DR

This paper calculates the universal electrical conductivity at a 2D superconductor-insulator transition, considering quenched disorder and Coulomb interactions, revealing how these factors influence self-duality and transport properties.

Contribution

It introduces a dual fermionic model with a Chern-Simons gauge field to analyze conductivity at the transition, including effects of disorder and Coulomb interactions.

Findings

Disorder and gauge fluctuations cause deviations from self-duality.

Coulomb interactions mitigate violations of self-duality.

Calculated universal conductivity near the transition.

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.