Quantum Theory of Quantum-Hall Smectics

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.