Quantum Theory of Quantum-Hall Smectics

TL;DR

This paper develops a quantum smectic model for anisotropic states in high Landau level fillings, predicting flow of Hall conductance and explaining transport properties with Luttinger liquid effects.

Contribution

It introduces a coupled-Luttinger-liquid model for quantum Hall smectics and analyzes their stability and transport properties, connecting theory with recent experimental observations.

Findings

Interaction terms may drive the system into an anisotropic Wigner crystal at low temperatures.

Hall conductance flows toward quantized values on either side of the filling range.

The semiclassical theory explains resistivity magnitudes and non-linearities in anisotropic quantum Hall states.

Abstract

We propose a quantum stripe (smectic) coupled-Luttinger-liquid model for the anisotropic states which occur in two-dimensional electron systems with high-index partial Landau level filling, $\nu^{*} = \nu - \lbrack\nu\rbrack$. Perturbative renormalization group calculations establish that interaction terms neglected in this model are relevant - probably driving the system into an anisotropic Wigner crystal---but for $0.4 \lesssim \nu^{*} \lesssim 0.6$ only below temperatures which are outside of the experimentally accessible range. We argue that the Hall conductance of the ground state flows toward $\lbrack\nu\rbrack e^{2}/h$ and $(\lbrack\nu\rbrack + 1) e^{2}/h$ respectively, on the low and high filling factor sides of this range, consistent with recent observations. A semiclassical theory of smectic state transport properties, which incorporates Luttinger liquid effects in the evaluation of scattering amplitudes, accounts for the magnitude of the dissipative resistivities at $\nu^{*}=1/2$, for their $\nu^{*}$-dependence, and for the observation of non-linearities of opposite sign in easy and hard direction resistivities.