Collective modes of quantum Hall stripes

The collective modes of striped phases in a quantum Hall system are compute d using the time-dependent Hartree-Focle approximation. Uniform stripe phas es are shown to be unstable to the formation of modulations along the strip es, so that within the Hartree-Fock approximation the ground state is a str ipe crystal. Such crystalline states are generically gapped at any finite w ave vector; however, in the quantum Hall system the interactions of modulat ions among different stripes is found to be remarkably weak, leading to an infinite collection of collective modes with immeasurably small gaps. The r esulting long wavelength behavior is derivable from an elastic theory for s mectic 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 factor s sufficiently far from 1/2, indicating a second-order phase transition. Th e modes contain several other signatures that should be experimentally obse rvable.