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

TL;DR

This paper investigates the phase transition between Laughlin liquid and Wigner solid in wide quantum wells, highlighting a high-density transition driven by effective interaction softening, using a model interaction approach.

Contribution

It introduces a method to compare ground-state energies using an effective interaction model in wide quantum wells, revealing a high-density Wigner solid transition.

Findings

High-density Wigner solid transition occurs in very wide wells.

Transition driven by softening of the effective interaction at short distances.

Low-density transition driven by Landau-level mixing.

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 $\nu$. 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 $\lambda$ 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.