Laughlin liquid - Wigner solid transition at high density in wide quantum wells

Abstract

Assuming that the phase transition between the Wigner solid and the Laughlin liquid is first-order, we compare ground-state energies to find features of the phase diagram at fixed $ν$. Rather than use the Coulomb interaction, we calculate the effective interaction in a square quantum well, and fit the results to a model interaction with length parameter $λ$ roughly proportional to the width of the well. We find a transition to the Wigner solid phase at high density in very wide wells, driven by the softening of the interaction at short distances, as well as the more well-known transition to the Wigner solid at low density, driven by Landau-level mixing.