Freezing of the quantum Hall liquid at $ν= $ 1/7 and 1/9

Abstract

We compare the free energy computed from the ground state energy and low-lying excitations of the 2-D Wigner solid and the fractional quantum Hall liquid, at magnetic filling factors $ν= 1/7$ and 1/9. We find that the Wigner solid melts into the fractional quantum Hall liquid at roughly the same temperature as that of some recent luminescence experiments, while it remains a solid at the lower temperatures characteristic of the transport experiments. We propose this melting as a consistent interpretation of both sets of experiments.