Fractional quantization of Hall resistance as a consequence of mesoscopic feedback

TL;DR

This paper introduces a nonlinear model incorporating mesoscopic feedback to explain the fractional quantization of Hall resistance, demonstrating that charge and flux quantization lead to exact integer and fractional Hall conductance values.

Contribution

The paper presents a novel nonlinear single-particle model with mesoscopic feedback that explains fractional quantum Hall resistance as a consequence of charge and flux quantization.

Findings

Exact integer and fractional quantization of Hall conductance derived

Hall resistance expressed as R_H = (h/2e^2)(M/N) at filling factor N/M

Model confirms the validity of mesoscopic mechanics in quantum physics

Abstract

A nonlinear single-particle model is introduced, which captures the characteristic of systems in the quantum Hall regime. The model entails the magnetic Shr\"odinger equation with spatially variable magnetic flux density. The distribution of flux is prescribed via the postulates of the mesoscopic mechanics (MeM) introduced in my previous articles [cf. J. Phys. Chem. Solids, 65 (2004), 1507-1515; J. Geom. Phys., Vol. 55/1 (2005), 1-18]. The model is found to imply exact integer and fractional quantization of the Hall conductance. In fact, Hall resistance is found to be $R_H = \frac{h}{2e^2}\frac{M}{N}$ at the filling factor value $N/M$. The assumed geometry of the Hall plate is rectangular. Special properties of the magnetic Shr\"odinger equation with the mesoscopic feedback loop allow us to demonstrate quantization of Hall resistance as a direct consequence of charge and flux quantization. I believe results presented here shed light at the overall status of the MeM in quantum physics, confirming its validity.