Interactions and Landau level mixing at large half odd-integer filling

Recent transport experiments on two-dimensional hole systems (2DHSs) in a strong perpendicular magnetic field show variations in the anisotropy of resistivity at half odd-integer filling fractions $\nu$=7/2, 9/2, and 11/2 that differ from those seen in two-dimensional electron systems \footnote[1]{M. J. Manfra et al., Phys. Rev. Lett. {\bf 98}, 206804 (2007).}. It has been suggested that spin-orbit coupling in 2DHSs leads to these unusual transport properties, as it gives rise to Landau level mixing. We consider the general problem of interacting fermions subject to a perpendicular magnetic field with Landau level mixing in the limit of large Landau levels, and discuss the effect of Landau level mixing on charge-density wave formation in comparison to the single Landau level case \footnote[2]{R. Moessner and J. T. Chalker, Phys. Rev. B. {\bf 54}, 5006 (1996).}. We study the case of spin-orbit induced mixing in detail, and discuss implications for experiments.