Stripe formation driven by space noncommutativity in quantum Hall systems

Abstract

We propose that the transport anisotropy observed in half-filled high Landau levels ($N\ge 2$) 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.

4 pages, no figures

References in corpus (15)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Noncommutative Field Theory
• Renormalization Group Approach to Interacting Fermions
• Evidence for an Anisotropic State of Two-Dimensional Electrons in High Landau Levels
• Charge Density Wave in Two-Dimensional Electron Liquid in Weak Magnetic Field
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Strongly Anisotropic Transport in Higher Two-Dimensional Landau Levels
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• The Ground State of a Two-Dimensional Electron Liquid in a Weak Magnetic Field
• Exact results for interacting electrons in high Landau levels
• Anisotropic States of Two-Dimensional Electron Systems in High Landau Levels: Effect of an In-Plane Magnetic Field
• Strongly Anisotropic Electronic Transport at Landau Level Filling Factor $\nu =9/2$ and $\nu =5/2$ Under Tilted Magnetic Field
• Phase structure of non-commutative scalar field theories
• Cooper Instability of Composite Fermions
• Renormalization Group Equations and the Lifshitz Point In Noncommutative Landau-Ginsburg Theory