Semi-analytical model of Hall resistance anomalies (overshooting) in the fractional quantized Hall effect

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 mu m) Hall bar is defined by top gates. A semi-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 via 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 can co-exist in 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 in Fabry-Perot type interference experiments. A gate defined narrow sample design is proposed to enhance the visibility of fragile effects like interference and overshooting based on our semi-analytical model.