Renormalization group analysis of superconductor-insulator transition with disorder

A recent experiment [1] indicates the magnetic field-tuned superconductor-insulator transition (SIT) in thin films can exhibit particle-vortex self-dual electrical conductivity. With the aim of understanding this quantum critical behavior, we consider a manifestly self-dual theory consisting of a Dirac fermion coupled to a Chern-Simons gauge field [2] in the presence of quenched disorder. We derive renormalization group fixed points of this theory in the presence of disorder and gauge fluctuations, which are controlled in an expansion in the number of fermion flavors. We then discuss the quantum critical conductivity of these fixed points. This formalism can also be used to understand quantum Hall plateau transitions.

[1] PNAS 113 (2) 280-285,2016
[2] Phys. Rev. B 95, 045118 (2017)