Geometric Resonance in Modulated Quantum Hall Systems Near $ \nu = 1/2$

TL;DR

This paper develops a theoretical explanation for observed resonance effects in magnetoresistance of modulated quantum Hall systems near filling factor 1/2, attributing them to geometric resonance of composite fermions with density modulation.

Contribution

It introduces a theory linking magnetoresistance features to geometric resonance of composite fermion orbits with density modulation in quantum Hall systems.

Findings

Resonance structures are due to geometric resonance of composite fermion orbits.

Minima and maxima in magnetoresistance arise from different physical mechanisms.

The theory explains observed experimental features near filling factor 1/2.

Abstract

We propose a theory for the new effects recently observed by Willett et al [1] in the magnetoresistance of a weakly modulated two dimensional electron gas near filling factor 1/2. Minima in transverse magnetoresistance and maxima in longitudinal magnetoresistance at the same magnetic field producing the new resonance structure are reported. The structure occurs due to geometric resonance of the composite fermion cyclotron orbits with the modulation period of the effective magnetic field $ B_{eff} $ due to the applied density modulation. The transverse minimum occurs due to the inhomogeneity in the field $ B_{eff} $ in the presence of density modulations, whereas the longitudinal maximum can arise due to a shape-effect (distortion) of the composite fermion Fermi surface (CF-FS). Thus the minima and maxima reflect different physical mechanisms. PACS numbers 71.10 Pm, 73.40 Hm, 73.20 Dx {}