Symmetry breaking by periodic potentials in quantum Hall systems

The quantum Hall system in a high Landau level under the influence of a one dimensional spatially periodic potential is investigated by direct diagonalization. We consider the N = 2 Landau level at half filling for finite systems with aspect ratio one. Hence the symmetry breaking, or lack thereof, is due to the periodic potential. In agreement with mean field and perturbation theory studies, direct diagonalization indicates that for weak potentials stripes order perpendicular to the external potential. At stronger values of the potential, the potential dominates and the periodicity seen is determined by the potential and not the stripes. An example is given where randomness tends to enhance the symmetry breaking induced by the periodic potential