Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations
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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 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 4He 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 nematic, tetratic, and hexatic generalizations of Laughlin's trial wave function having twofold, fourfold, and sixfold broken rotational symmetry, respectively. In the limit of zero wave vector q the dispersion of these modes is singular, with a gap that is dependent on the direction along which q=0 is approached for nematic and tetratic liquid crystalline states, but remains regular in the hexatic state, as permitted by the fourth order wave-vector dependence of the (projected) oscillator strength and static structure factor.
Phys. Rev. B 73, 085314 (2006)