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Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations

Cintia M. Lapilli·Carlos Wexler
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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 $^4$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.

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Cintia M. Lapilli, Carlos Wexler. 2006-02-09. Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations. https://doi.org/10.1103/physrevb.73.085314

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