Hall resistance anomalies in the integer and fractional quantum Hall regime

Abstract

Experimental evidence of resistance anomalies in the high-mobility two-dimensional electron gas (2DEG) formed in the GaAs/AlGaAs heterostructure, in the integer and fractional quantized Hall regime, is shown. The data complement to a good approximation the semianalytic calculations used to describe the formation of integral and fractional incompressible strips. The widths of current-carrying channels were calculated by incorporating the screening properties of the 2DEG and the effect of a magnetic field in the perpendicular mode. The many-body effects of the composite fermions are taken into consideration for the energy gap for the fractional states. It is shown that incompressible strips at the edges for both integer and fractional filling factors coexist in their evanescent phase for a particular range of magnetic fields, resulting in overshoot effects at the Hall resistance. Specifically, anomalous Hall resistances were noticed for filling factors $\ensuremath{\nu}$ = $\frac{4}{3}$, $\frac{3}{2}$, $\frac{5}{3}$, $\frac{8}{3}$, 3, $\frac{10}{3}$, $\frac{7}{2}$, and 5. This effect is explained and discussed using the screening theory.