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

TL;DR

This paper uses the single mode approximation to calculate collective excitation spectra in quantum Hall liquid crystals with different symmetries, revealing anisotropic gaps and dispersion behaviors.

Contribution

It introduces SMA calculations of collective modes in nematic, tetratic, and hexatic quantum Hall liquid crystal states with broken rotational symmetries.

Findings

Nematic and tetratic states exhibit direction-dependent gaps at zero wavevector.

Hexatic state shows regular dispersion with no singularities.

Dispersion characteristics depend on the type of liquid crystalline order.

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.