Vortex variable range hopping in a conventional superconducting film

The behavior of a disordered amorphous thin film of superconducting indium oxide has been studied as a function of temperature and magnetic field applied perpendicular to its plane. A superconductor-insulator transition has been observed, though the isotherms do not cross at a single point. The curves of resistance versus temperature on the putative superconducting side of this transition, where the resistance decreases with decreasing temperature, obey two-dimensional Mott variable-range hopping of vortices over wide ranges of temperature and resistance. To estimate the parameters of hopping, the film is modeled as a granular system and the hopping of vortices is treated in a manner analogous to hopping of charges. The reason the long-range interaction between vortices over the range of magnetic fields investigated does not lead to a stronger variation of resistance with temperature than that of two-dimensional Mott variable-range hopping remains unresolved.