Optimal orientation of striped states in the quantum Hall system against external modulations

We study striped states in the quantum Hall system around half-filled high Landau levels and obtain the optimal orientation of the striped state in the presence of an external unidirectional periodic potential. It is shown that the optimal orientation is orthogonal to the external modulation in the Coulomb dominant regime ( the orthogonal phase) and is parallel in the external modulation dominant regime ( the parallel phase). The phase boundary of these two phases is determined numerically in the parameter space of the strength and wave number of the external modulation at the half-filled third Landau level.