Disclination Unbinding Transition in Quantum Hall Liquid Crystals

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.

Added explanation for spin dependence of anisotropic strength: The reason for this spin oscillation is simple: in the energetics of Eqs. (4-6), there is an energy scale $e^2/l_b$ that decreases with increasing filling factor $\nu$; simultaneously the matrix elements of the Coulomb interaction [Eq. (3)] increase with increasing LL index $L$, resulting in the observed spin dependence

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