Quantum Hall effect in a vortex liquid

A two-dimensional superconducting film in a magnetic field is considered in the adiabatic limit when vortex dynamics is dominated by the Magnus force. By mapping a vortex liquid state into that of electrons in an effective magnetic field, I find that the Hall conductance is quantized as σxy=(4e²/h)[1+n(2m-1)]/n with n,m{≥}1 integers, predicting a fractional quantum Hall effect in a boson system. This phenomenon can also account for observed steps in the magnetization curve of YBa₂{Cu}₃O_7-δ. The feasibility of a vortex liquid, i.e., melting of a flux lattice at T=0 by quantum fluctuations, is studied.