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, ${\nu }^{\ast }=\nu -[\nu ]$. 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 $0.4\lesssim {\nu }^{\ast }\lesssim 0.6$ only below temperatures which are outside of the experimentally accessible range. We argue that the Hall conductance of the ground state flows toward $[\nu ]e^2/h$ and $([\nu ]+1)e^2/h$ 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 ${\nu }^{\ast }=1/2$, for their ${\nu }^{\ast }$-dependence, and for the observation of non-linearities of opposite sign in easy and hard direction resistivities.

12 pages, 7 figures included, submitted to Phys. Rev. B

References in corpus (1)

• Unlocking Transition for Modulated Surfaces and Quantum Hall Stripes

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