Vortex variable-range-hopping resistivity in superconducting films

We study both classical and quantum vortex creep in disordered thin-film superconductors in an applied magnetic field. Quantum tunneling of vortices leads to a variable-range-hopping resistivity with a non-Arrhenius temperature dependence at low T. Mott’s 1/3 law is modified by long-range vortex interactions, and a numerical analysis enables us to estimate a temperature exponent between roughly 2/3 and 4/5. At higher T, a classical hopping regime is expected with a current-density scale for nonlinearities varying (roughly) as ${\mathit{T}}^3$.