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

TL;DR

This paper compares the free energies of the 2D Wigner solid and fractional quantum Hall liquid at specific filling factors, proposing a temperature-driven melting transition that explains experimental observations.

Contribution

It introduces a comparative analysis of free energies to interpret the melting of the quantum Hall liquid at certain filling factors, linking theory with experiments.

Findings

Wigner solid melts into the fractional quantum Hall liquid near experimental temperatures.

The solid remains at lower temperatures typical of transport experiments.

The melting transition explains both luminescence and transport experimental results.

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 $\nu = 1/7$ 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.