Role of disorder in half-filled high Landau levels

We study the effects of disorder on the quantum Hall stripe phases in half-filled high Landau levels using exact numerical diagonalization. We show that, in the presence of weak disorder, a compressible, striped charge-density wave, becomes the true ground state. The projected electron-density profile resembles that of a smectic liquid. With increasing disorder strength W, we find that there exists a critical value, $W_c\sim {0.12e}^2/\epsilon \mathcal{l},$ where a transition/crossover to an isotropic phase with strong local electron-density fluctuations takes place. The many-body density of states are qualitatively distinguishable in these two phases and help elucidate the nature of the transition.