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

Salman, Aysevil; Mese, A.I.; Yücel, Melike Behiye; Siddiki, A.

doi:10.1140/epjb/e2013-30758-3

Cited by 5 publications

(29 citation statements)

References 58 publications

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“…15 specifically predicts that the overshoot effect can be manipulated by changing the electrostatic edge profile of the electron gas, for example by utilizing side gates. In a very recent work, overshoot effect is also predicted for the fractional states and is investigated within the screening theory16.…”

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confidence: 99%

“…The result are regions of varying carrier density profile (the compressible strips), where the total potential is flat, and regions of constant carrier density profile (the incompressible strips), where the total potential varies. The width of the k th incompressible strip (with local filling factor k ) can be evaluated up to a reasonable approximation by an analytic formula16 where κ is the dielectric constant (~12.4, for GaAs), and n ( x ) is the electron density at B = 0 as a function of lateral coordinate x . Here, the density gradient is evaluated at the center of the k th incompressible strip, x k .…”

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confidence: 99%

“…For odd (even) filling factor the energy gap is Δ E odd = g * μ B B (). The local carrier density distribution at zero magnetic field can be obtained within self-consistent numerical calculations1624 where l d is the depletion length and n 0 is the bulk electron density far away from the edges. The parameter t defines the distance from the edge at which the electron density reaches n 0 , in units of the effective Bohr radius .…”

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Anomalous resistance overshoot in the integer quantum Hall effect

Kendirlik

Sirt

Kalkan

et al. 2013

Sci Rep

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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...

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Anomalous resistance overshoot in the integer quantum Hall effect

Kendirlik

Sirt

Kalkan

et al. 2013

Sci Rep

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“…In contrast, the screening theory which takes into account the Coulomb interactions between charged carriers seems to illustrate this phenomenon within a framework which follows closely the experimental observations and how it changes with strong magnetic fields [15][16][17][18][19]. This was initially proposed in a qualitative manner by Beenakker [20] and Chang [21] considering the electron gas being divided into strips which alternate between incompressible (IS) and compressible (CS) states.…”

Section: Hall Resistance Anomaly (Overshoot)mentioning

confidence: 95%

“…However, within this framework the calculations are performed in a non-self-consistent manner. Additionally, assumptions like the 2DEG being located at the plane of z = 0 and the electrons being depleted by in-plane metallic gates on the same plane and generally having an oversimplified picture on the boundary conditions lead to an unrealistic model with wide ISs [17,23].…”

Section: Hall Resistance Anomaly (Overshoot)mentioning

confidence: 99%

Hall resistance anomalies in the integer and fractional quantum Hall regime

et al. 2020

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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 manybody 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 ν = 4 3 , 3 2 , 5 3 , 8 3 , 3, 10 3 , 7 2 , and 5. This effect is explained and discussed using the screening theory.

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Classical and quantum capacitances calculated locally considering a two-dimensional Hall bar

Guvenilir

Kılıcoglu

Eksi

et al. 2019

Physica E: Low-dimensional Systems and Nanostructures

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In this work we investigate the electrostatic properties of two dimensional electron system (2DES) in the integer quantum Hall regime. The alternating screening properties of compressible and incompressible strips are formed due to edge effects together with electron-electron interactions. As it is well known, the Landau quantization emanates from strong perpendicular magnetic fields. The (Landau) energy levels are broadened due to impurities, which we embedded their effects in density of states (DOS). In a basic level DOS has two different forms: the Gaussian and semi-elliptic descriptions. The second form is calculated within the self consistent Born approximation (SCBA). Having in hand the density of states, we obtain both the longitudinal and Hall (transversal) conductivities (σ l , σ H ) utilizing Thomas-Fermi-Poisson approximation to calculate position dependent charge density profile and use Drude formalism to obtain transport coefficients. Since, the definition of capacitance is closely related with compressibility via DOS, (local) screening properties of 2DES is extremely important to understand local capacitances. Here we numerically simulate a translational invariant Hall bar subject to high magnetic fields which is perpendicular to the plane of the 2DES using realistic parameters extracted from the related experiments. Using the above mentioned approaches the local capacitances are calculated, numerically. Our findings are in perfect agreement with related experimental results which are based on a dynamic scanning capacitance microscopy technique.

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

Cited by 5 publications

References 58 publications

Anomalous resistance overshoot in the integer quantum Hall effect

Anomalous resistance overshoot in the integer quantum Hall effect

Hall resistance anomalies in the integer and fractional quantum Hall regime

Classical and quantum capacitances calculated locally considering a two-dimensional Hall bar

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