Universal conductivity of two-dimensional films at the superconductor-insulator transition

The zero-temperature universal conductivity of two-dimensional (2D) films at the supeconductor-insulator transition is studied. The existence of a finite conductivity at T=0 and the universality class for this transition is discussed. Neglecting disorder as a first approximation, so the transition is from a commensurate Mott-Hubbard insulator to a superconductor, we calculate analytically the universal conductivity for the 2D pure boson Hubbard model up to the first order in a large-N expansion and numerically by Monte Carlo simulation of the (2+1)-D XY model. From the Monte Carlo results we find the universal conductivity to be ${\mathrm{\sigma }}^{\mathrm{*}}$=(0.285±0.02)${\mathrm{\sigma }}_{\mathit{Q}}$, where ${\mathrm{\sigma }}_{\mathit{Q}}^{\mathrm{-}1}$==${\mathit{R}}_{\mathit{Q}}$==h/(2e${)}^2$≊6.45 kΩ. An analysis in 1D suggests that in the presence of disorder, the universal conductivity in films might be somewhat smaller than this value. The possible existence of universal dissipation in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films is also discussed briefly.