Anomalous resistance overshoot in the integer quantum Hall effect

Abstract

In this work we report on experiments performed on smooth edge-narrow Hall bars. The magneto-transport properties of intermediate mobility two-dimensional electron systems are investigated and analyzed within the screening theory of the integer quantized Hall effect. We observe a non-monotonic increase of Hall resistance at the low magnetic field ends of the quantized plateaus, known as the overshoot effect. Unexpectedly, for Hall bars that are defined by shallow chemical etching the overshoot effect becomes more pronounced at elevated temperatures. We observe the overshoot effect at odd and even integer plateaus, which favor a spin independent explanation, in contrast to discussion in the literature. In a second set of the experiments, we investigate the overshoot effect in gate defined Hall bar and explicitly show that the amplitude of the overshoot effect can be directly controlled by gate voltages. We offer a comprehensive explanation based on scattering between evanescent incompressible channels.T he overwhelming interest to utilize quantum mechanics in applied technologies finds one of its first manifestations in the integer quantized Hall effect (IQHE) 1 . The magnetic field dependence of the transport coefficients of a two dimensional electron system (2DES) provides a possibility to standardize resistance in units of the von Klitzing constant h/e 2 , where h is the Planck constant and e is the elementary charge. However, an unexpected non-monotonic magnetic field dependence of the Hall resistance at the low-field-end of the quantized plateaus, known as the overshoot effect, remains a puzzle despite of both theoretical and experimental efforts in various material systems including GaAs/AlGaAs heterostructure 2-6 as well as Si/SiGe 7-13 and Si metal oxide semiconductor field effect transistors 14 . The utilization of the quantized Hall effect as a resistance standard is hindered by such anomalies, especially because their physical mechanism is not well understood. The overshoot effect is observed in these material systems at various filling factors n, defined by the number of occupied quantized (spin resolved) Landau levels (LL) below the Fermi energy. The effect has already been observed in the 1980's, where its physical mechanism was attributed to non-ideal contacts 2-4 , but without providing clear evidence for this hypothesis. Later, the overshoot effect was attributed to the decoupling of the spin-split states within the same LL at odd filling factors by Richter and Wheeler 5 , or, alternatively by the scattering between edge states together with spin-orbit interaction by Komiyama and Nii 6 . Recently, the overshoot effect has been investigated in Si/SiGe heterostructures as a function of current and temperature 12 . These experimental results have been elegantly explained within the screening theory of the integer quantized Hall effect, which explicitly takes into account the direct Coulomb interaction between charge carriers. In this approach the overshoot effect is described using co-existing (curr...

Conductance quantization suppression in the quantum Hall regime

“…The condition for a stable strip of width a k with level index k requires , where is the magnetic length. Although the stability/collapse of an incompressible strip is a direct finding of a self-consistent calculation, a rough estimate of the stability condition can be done from electrostatic calculations by Chklovskii et al 4 , 7 . According to this theory, a k is estimated by the equation: where n el ( x ) is the electron density across the device at | B | = 0 T, ε is the dielectric constant of the insulating material, is the charge density gradient evaluated at the center of the k th incompressible strip, and E k is the Landau spectrum.…”

Hall resistance anomalies in the integer and fractional quantum Hall regime

“…An important observation is that the B positions of the minima observed in the R xx measurement match the B positions where the maximum width of the ISs is located by using the Eqs. (6) and (8) for the integer ISs and the equivalent ones for the fractional states, as seen in Figs. 3 and 4.…”

“…Subsequent work from Lier and Gerhardts [24] and Siddiki et al [25] combat this by modifying the Chklovskii model with self-consistent calculations and taking into account the Hall bar geometry and chemical etching of the mesa structures, matching, to a great extent, the experimental work in the regime of the IQHE. Examples of experimental work on the IQHE can be found in the works of Sailer et al [15] and Kendirlik et al [6], where Si/SiGe and GaAs/AlGaAs heterostructures were used, respectively. Some varied results on the temperature behavior of the resistance overshoot effect have been noticed which can be explained by two types of screening models, "the bulk" and "the edge" models [15].…”

“…Since the discovery of the integer/fractional quantum Hall effect (IQHE/FQHE) [1,2], the study of quantum states in the two-dimensional electron gas (2DEG) systems has sparked great interest, particularly utilizing its quantum-mechanical properties for applications in quantum computing [3]. However, a universal theory has still not materialized to explain the various anomalous phenomena that appear in experimental studies such as the anomalous Hall resistance (overshooting) [4][5][6]. The resistance overshooting is the observance of an anomalous increase in resistance at a plateau corresponding to a specific filling factor ν observed within the transverse resistance of the IQHE/FQHE.…”

The local nature of incompressibility of quantum Hall effect

“…At T →0, where only electrons at E F contribute to current, this thermodynamic consideration is meaningless at length scales below the Fermi wavelength λ F . From this thermodynamical point of view it is reasonable to expect that incompressible strips narrower than λ F becomes transparent due to scattering between neighbouring compressible regions18. In this situation, V L becomes finite and V H deviates from its quantized value.…”