Geometry of Compressible and Incompressible Quantum Hall States: Application to Anisotropic Composite Fermion Liquids

TL;DR

This paper extends Haldane's geometric framework to compressible quantum Hall states, linking anisotropy in the composite fermion Fermi surface to the intrinsic geometry, and validates the model with experimental data.

Contribution

It introduces a simple model to exactly determine geometric parameters from electron mass anisotropy, generalizing the geometric description to compressible states.

Findings

Model accurately predicts anisotropy in composite fermion Fermi surface

Results align with recent experimental measurements

Provides broader implications for quantum Hall state geometry

Abstract

Haldane's geometrical description of fractional quantum Hall states is generalized to compressible states. It is shown that anisotropy in the composite fermion Fermi surface is a direct reflection of this intrinsic geometry. A simple model is introduced in which the geometric parameter can be obtained exactly from other parameters including electron mass anisotropy. Our results compare favorably with recent measurements of anisotropy in composite fermion Fermi surface [D. Kamburov, Y. Liu, M. Shayegan, L. N. Pfeiffer, K. W. West, and K. W. Baldwin, Phys. Rev. Lett. 110, 206801 (2013)]. Broader implications of our results are discussed.