Disclination Unbinding Transition in Quantum Hall Liquid Crystals

TL;DR

This paper develops an elastic theory for quantum Hall liquid crystals, showing how dislocation unbinding causes a phase transition from nematic to isotropic, aligning with experimental observations of resistivity anisotropies.

Contribution

It introduces a long-wavelength elastic model derived from Hartree-Fock theory, linking dislocation unbinding to phase transitions in quantum Hall liquid crystals.

Findings

Transition temperatures match experimental data

Dislocations induce a nematic to isotropic phase transition

Large resistivity anisotropies observed in experiments

Abstract

We derive the the long-wavelength elastic theory for the quantum Hall smectic state starting from the Hartree-Fock approximation. Dislocations in this state lead to an effective nematic model for $T>0$, which undergoes a disclination unbinding transition from a phase with algebraic orientational order into an isotropic phase. We obtain transition temperatures which are in qualitative agreement with recent experiments which have observed large anisotropies of the longitudinal resistivities in half-filled Landau levels, lending credence to the liquid crystal interpretation of experiments.