Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations
arXiv:cond-mat/0506740 · doi:10.1103/PhysRevB.73.085314
Abstract
A variety of recent experiments probing the low-temperature transport properties of quantum Hall systems have suggested an interpretation in terms of liquid crystalline mesophases dubbed {\em quantum Hall liquid crystals}. The single mode approximation (SMA) has been a useful tool for the determination of the excitation spectra of various systems such as phonons in He and in the fractional quantum Hall effect. In this paper we calculate (via the SMA) the spectrum of collective excitations in a quantum Hall liquid crystal by considering {\em nematic}, {\em tetratic}, and {\em hexatic} generalizations of Laughlin's trial wave function having two-, four- and six-fold broken rotational symmetry, respectively. In the limit of zero wavevector $\qq$ the dispersion of these modes is singular, with a gap that is dependent on the direction along which $\qq=0$ is approached for {\em nematic} and {\em tetratic} liquid crystalline states, but remains regular in the {\em hexatic} state, as permitted by the fourth order wavevector dependence of the (projected) oscillator strength and static structure factor.
6 pages, 5 eps figures included
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