Resistivity in Quantum Vortex Liquid of Clean Two-Dimensional Superconductor

Motivated by a recent controversy on a possible quantum phase in thin films of relatively clean superconductors under an out-of-plane magnetic field, the quantum fluctuation effects on the phase diagram and the resistivity are reexamined. It is argued that most of features seen in the corresponding resistivity data in relatively clean systems reported recently are explained within the present theory, and that the fan-shaped resistivity curves, suggestive of the presence of a superconductor to insulator transition at zero temperature, in the vortex liquid regime is a consequence of the insulating behavior of the Aslamasov-Larkin fluctuation conductivity in the quantum regime.