Stripe formation driven by space noncommutativity in quantum Hall systems

TL;DR

This paper suggests that space noncommutativity, related to quantum uncertainty, causes stripe formation in quantum Hall systems at specific half-fillings, explaining observed transport anisotropy.

Contribution

It introduces the idea that space noncommutativity drives stripe formation in quantum Hall systems at certain half-fillings, supported by renormalization group analysis.

Findings

Stripe formation occurs at half-fillings $ u=9/2, 11/2, 13/2$ due to noncommutativity.

Noncommutativity effect explains transport anisotropy in high Landau levels.

Analysis aligns with experimental observations.

Abstract

We propose that the transport anisotropy observed in half-filled high Landau levels ($N \geq 2$) is caused by the space noncommutativity effect, namely the Heisenberg uncertainty relation between the spatial coordinates of electrons. The stripe corresponds to a limit that one coordinate of a large number of particles is fixed at a certain value while its conjugate coordinate is completely uncertain. We make a renormalization group analysis and find that the noncommutativity effect is able to drive the stripe formation only at half-fillings $\nu = 9/2, 11/2, 13/2,$ etc., in agreement with experiments.