Collective modes of quantum Hall stripes

The collective modes of striped phases in a quantum Hall system are computed using the time-dependent Hartree-Focle approximation. Uniform stripe phases are shown to be unstable to the formation of modulations along the stripes, so that within the Hartree-Fock approximation the ground state is a stripe crystal. Such crystalline states are generically gapped at any finite wave vector; however, in the quantum Hall system the interactions of modulations among different stripes is found to be remarkably weak, leading to an infinite collection of collective modes with immeasurably small gaps. The resulting long wavelength behavior is derivable from an elastic theory for smectic liquid crystals. Collective modes for the phonon branch are computed throughout the Brillouin zone, as are spin-wave and magnetoplasmon modes. A soft mode in the phonon spectrum is identified for partial filling factors sufficiently far from 1/2, indicating a second-order phase transition. The modes contain several other signatures that should be experimentally observable.