An analytical model of fractional overshooting

TL;DR

This paper presents an analytical model predicting resistance anomalies in high mobility 2D electron systems within the fractional quantum Hall regime, explaining fractional incompressible strips and overshoot phenomena.

Contribution

It introduces a new analytical calculation scheme incorporating many-body effects and screening to describe fractional incompressible strips and resistance overshoot in fractional quantum Hall systems.

Findings

Fractional incompressible strips become evanescent and coexist, causing Hall resistance overshoot.

The model explains the absence of the 1/3 state in Fabry-Perot interference.

Proposes a sample design to observe fragile interference effects.

Abstract

We predict resistance anomalies to be observed at high mobility two dimensional electron systems (2DESs) in the fractional quantized Hall regime, where the narrow (L <10 ?m) Hall bar is defined by top gates. An analytic calculation scheme is used to describe the formation of integral and fractional incompressible strips. We incorporate the screening properties of the 2DES, together with the effects of perpendicular magnetic field, to calculate the effective widths of the current carrying channels. The many-body effects are included to our calculation scheme through the energy gap obtained from the well accepted formulation of the composite fermions. We show that, the fractional incompressible strips at the edges, assuming different filling factors, become evanescent and co-exist at certain magnetic field intervals yielding an overshoot at the Hall resistance. Similar to that of the integral quantized Hall effect. We also provide a mechanism to explain the absence of 1/3 state at the Fabry-Perot interference experiments. Yet, an un-investigated sample design is proposed to observe and enhance the fragile effects like interference and overshooting based on our analytical model.