Crystallization in the Fractional Quantum Hall Regime Induced by Landau-level Mixing

TL;DR

This paper investigates how Landau level mixing influences the crystallization of two-dimensional electrons in high magnetic fields, revealing a phase diagram with a strong dependence on filling factors and explaining experimental differences in GaAs quantum wells.

Contribution

It provides the first non-perturbative phase diagram of Wigner crystal formation considering Landau level mixing effects in the fractional quantum Hall regime.

Findings

Crystallization is more likely away from magic filling factors due to Landau level mixing.

The phase boundary shows a strong dependence on the filling factor ν.

Predicted a transition to a strongly correlated crystal of composite fermions near ν=1/5 and 2/9.

Abstract

The interplay between strongly correlated liquid and crystal phases for two-dimensional electrons exposed to a high transverse magnetic field is of fundamental interest. Through the non-perturbative fixed phase diffusion Monte Carlo method, we determine the phase diagram of the Wigner crystal in the $\nu-\kappa$ plane, where $\nu$ is the filling factor and $\kappa$ is the strength of Landau level mixing. The phase boundary is seen to exhibit a striking $\nu$ dependence, with the states away from the magic filling factors $\nu=n/(2pn+1)$ being much more susceptible to crystallization due to Landau level mixing than those at $\nu=n/(2pn+1)$. Our results explain the qualitative difference between the experimental behaviors observed in n-doped and p-doped GaAs quantum wells, and, in particular, the existence of an insulating state for $\nu<1/3$ and also for $1/3 <\nu< 2/5$ in low density p-doped systems. We predict that in the vicinity of $\nu=1/5$ and $\nu=2/9$, increasing LL mixing causes a transition not into an ordinary electron Wigner crystal but rather into a strongly correlated crystal of composite fermions carrying two vortices.