Simulation of quantum melting of the vortex lattice and of fractional quantum Hall-like states of the quantum vortex liquid in 2D superconductors

We present results of quantum path-integral Monte Carlo studies of quantum melting of the Abrikosov vortex lattice in a two-dimensional (2D), undamped, Magnus-force model superconductor. The dependence of the melting field, B-m, on the vortex mass, is found to obey the simple scaling law proposed by Magro and Ceperley. In the quantum vortex liquid state for B > B-m, we find a series of maxima in the vortex-vortex correlation function, measured through the intensity of the first Bragg peak, as a function of the strength of the Magnus force in the underdamped limit. These provide the first evidence of the existence of fractional quantum Hall-like states for the 2D quantum vortex liquid.