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

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 $ν-κ$ plane, where $ν$ is the filling factor and $κ$ is the strength of Landau level mixing. The phase boundary is seen to exhibit a striking $ν$ dependence, with the states away from the magic filling factors $ν=n/(2pn+1)$ being much more susceptible to crystallization due to Landau level mixing than those at $ν=n/(2pn+1)$. 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 $ν<1/3$ and also for $1/3 <ν< 2/5$ in low density p-doped systems. We predict that in the vicinity of $ν=1/5$ and $ν=2/9$, 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.