Electronic transport and the localization length in the quantum Hall effect

Furlan, Miha

doi:10.1103/physrevb.57.14818

Cited by 87 publications

(93 citation statements)

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“…With this direct access to ξ ∝ 1/T 0 it is possible to test for scaling behavior of ξ at the edges of the plateau as long as we are careful enough to stay within the localized regime. Earlier experiments confirmed the expected temperature dependence of σ xx (T ) and extracted ξ in the QHEregime [26,27], but either did not analyze the scaling behavior or were restricted to a small filling factor range close to the quasi-metallic regime. In a recent experiment on the QH plateau-insulator transition VRH conductivity following Eq.…”

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confidence: 51%

Hopping Conductivity in the Quantum Hall Effect: Revival of Universal Scaling

2002

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We have measured the temperature dependence of the conductivity σxx of a two-dimensional electron system deep into the localized regime of the quantum Hall plateau transition. Using variable-range hopping theory we are able to extract directly the localization length ξ from this experiment. We use our results to study the scaling behavior of ξ as a function of the filling factor distance |δν| to the critical point of the transition. We find for all samples a power-law behavior ξ ∝ |δν| −γ with a universal scaling exponent γ = 2.3 as proposed theoretically.PACS numbers: 73.40. Hm, 71.23.An, 72.20.My, 71.30.+h The prominent feature of the quantum Hall effect (QHE) is the emergence of quantized plateaus in the Hall resistance of a two-dimensional electron system (2DES) reflecting the localization of states at the Fermi edge. A deeper understanding of this fascinating phenomenon is gained from regarding the transition region between adjacent QHE plateaus [1,2]. In this regime the dissipative transport is governed by the delocalized states in the vicinity of the Landau level center. The degree of localization is expressed by the localization length ξ denoting the typical extension of the electron wave function. For any sample with a finite size L theory predicts the conductivity tensor in the plateau transition to follow a scaling function f (L/ξ) with a diverging localization length ξ = |δν| −γ [3] where δν = ν − ν c denotes the filling factor distance to the critical point ν c of the transition. The critical exponent γ = 2.3 was predicted to be universal, its value determined numerically [4] and validated by variation of the sample size [5]. Experimentally the scaling of the conductivity near the critical point was verified with great success for different samples by temperature, current, and frequency dependent measurements of the transition width [6,7,8]. These new parameters introduce effective lengths, and L f ∝ f 1/z and thereby add additional exponents z and p. These effective lengths replace the physical sample size L in the scaling functions f (L/ξ). Recent experiments extended the focus to the transition from the quantum Hall state to the Hall insulator [9,10,11]. In these investigations striking similarities to the scaling behavior in the transition between different QH states were observed [12] hinting to the same universality class for both types of transitions [13,14].In spite of the great success of scaling theory in the QHE there are still some experiments not fitting into the picture of universality. Non-universal exponents were observed in the dependence of the transition width on temperature [15], current [16] and frequency [17]. Other experiments seem to contradict scaling theory at all, both for the Hall plateau-insulator transition [18] and the transition between QHE plateaus [19,20].However, before making conclusions on a general failure of scaling theory it has to be considered that nearly all experiments do not measure the localization length ξ directly. Therefore an assumption about the ...

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confidence: 51%

Hopping Conductivity in the Quantum Hall Effect: Revival of Universal Scaling

2002

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“…Qualitatively, the absolute error in the quantization of ρ xy due to a finite ρ xx , can be estimated as ∆ρ xy = −sρ xx , where s is in the order of unity [14].…”

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Quantum resistance metrology in graphene

Giesbers

Rietveld

Houtzager

et al. 2008

Applied Physics Letters

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We have performed a metrological characterization of the quantum Hall resistance in a 1 µm wide graphene Hall-bar. The longitudinal resistivity in the center of the ν = ±2 quantum Hall plateaus vanishes within the measurement noise of 20 mΩ upto 2 µA. Our results show that the quantization of these plateaus is within the experimental uncertainty (15 ppm for 1.5 µA current) equal to that in conventional semiconductors. The principal limitation of the present experiments are the relatively high contact resistances in the quantum Hall regime, leading to a significantly increased noise across the voltage contacts and a heating of the sample when a high current is applied. The Hall resistance in two-dimensional electron systems (2DESs) is quantized in terms of natural constants only, R H = h/ie 2 with i an integer number [1]. Due to its high accuracy and reproducibility this quantized Hall resistance in conventional 2DESs is nowadays used as a universal resistance standard [2].Recently a new type of half-integer quantum Hall effect [3,4] was found in graphene, the purely twodimensional form of carbon [5]. Its unique electronic properties [6] (mimicking the behavior of charged chiral Dirac fermions [7,8]) allow the observation of a quantized Hall resistance up to room-temperature [9, 10], making graphene a promising candidate for a high-temperature quantum resistance standard. Although the quantized resistance in graphene around the ν = 2 plateau is generally believed to be equal to h/2e 2 , up to now it has not been shown to meet a metrological standard. In this Letter we present results of the first metrological characterization of the quantum Hall resistance in graphene. In particular, we will address the present accuracy of quantization (15 ppm) and the experimental conditions limiting this accuracy.Our sample consists of a graphene Hall-bar on a Si/SiO 2 substrate forming a charge-tunable ambipolar field-effect transistor (A-FET), where the carrier concentration can be tuned with a back-gate voltage V g [11]. In order to remove most of the surface dopants that make graphene generally strongly hole doped and limit its mobility, we have annealed the sample in-situ for several hours at 380 K prior to cooling it down slowly (∆T /∆t < 3 K/min) to the base temperature (0.35 K) of a toploading 3 He-system equipped with a 15 T superconducting magnet. After annealing, the charge neutrality point in the A-FET was situated at 5 V and the sample dis- * Electronic address: J.Giesbers@science.ru.nl † Electronic address: U.Zeitler@science.ru.nl 2 µm

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“…A similar discrepancy between W eff and W was observed in Refs. [14,21], again suggesting a very inhomogeneous current distribution in the samples. Whereas the bootstrap electron heating theory is most widely accepted to account for the breakdown of the QHE [13], here the underlying VRH mechanism alone is sufficient to explain the observed R xx ðBÞ dependence.…”

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confidence: 94%

“…Here, σ 0 is a parameter, T 0 is the hopping temperature, which is related to the localization length ξ by the relation k B T 0 ¼ Ce 2 =4πϵ r ϵ 0 ξ, ϵ 0 is the vacuum dielectric constant, ϵ r ≃ 7 is the relative dielectric constant averaged between the dielectric constants of the resist and SiC, and C ≃ 6.2 is a constant [20,21]. VRH has already been observed in various graphene samples below T ¼ 100 K [14,[22][23][24].…”

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Puddle-Induced Resistance Oscillations in the Breakdown of the Graphene Quantum Hall Effect

et al. 2016

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We report on the stability of the quantum Hall plateau in wide Hall bars made from a chemically gated graphene film grown on SiC. The ν ¼ 2 quantized plateau appears from fields B ≃ 5 T and persists up to B ≃ 80 T. At high current density, in the breakdown regime, the longitudinal resistance oscillates with a 1=B periodicity and an anomalous phase, which we relate to the presence of additional electron reservoirs. The high field experimental data suggest that these reservoirs induce a continuous increase of the carrier density up to the highest available magnetic field, thus enlarging the quantum plateaus. These in-plane inhomogeneities, in the form of high carrier density graphene pockets, modulate the quantum Hall effect breakdown and decrease the breakdown current. DOI: 10.1103/PhysRevLett.117.237702 Graphene [1,2] shows a unique half-integer quantum Hall effect (QHE) with conductivity plateaus σ xy ¼ 4ðm þ 1=2Þe 2 =h, where the factor 4 stands for the spin and valley degeneracies and m ¼ 0; AE1; AE2; … [3]. The peculiar dispersion E m ≃ AE420 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi jmjB½T p K of the Landau levels (LLs) in graphene induces large energy gaps at low LL indices and allows us to explore exotic transport phenomena even at relatively high temperature [4]. The substrate graphene is deposited on plays a central role in determining the features of the observed QHE. In lowmobility graphene on SiO 2 , the presence of electron-hole puddles at the charge neutrality point (CNP) prevents any divergence of the longitudinal resistance at filling factor ν < 2, whereas the Hall resistivity fluctuates around zero due to charge compensation [5]. On the other hand, in high mobility graphene deposited on boron nitride flakes, a complete degeneracy lifting of the Landau levels can be observed and the corresponding spin-valley textures have been identified [6,7]. In this Letter, we consider graphene deposited on top of a SiC substrate (G=SiC). In this system, the quantum Hall plateau at h=2e 2 is exceptionally robust with respect to magnetic field [8]. Moreover, G=SiC shows metrological quantum Hall quantization, with relative accuracies of the quantized resistance better than 10 −9 [9], even at lower magnetic fields and higher temperatures than GaAs-based quantum Hall resistance standards [10]. In this context, it is important to unveil the role of charge reservoirs in the stabilization of the first quantum Hall plateau [11,12] and to identify the mechanisms governing the breakdown of the QHE [8,13,14].In the following, we report on the results obtained from graphene samples grown by Graphensic AB company on the Si face of a 4H-SiC substrate. The details concerning the growth conditions can be found in Ref. [15]. The samples are tailored into Hall bar geometry with a width W ¼ 100 μm and a total length of 420 μm. The as-grown carrier density of G=SiC is of the order of 1 × 10 13 cm −2 and is reduced to about ≃5 × 10 11 cm −2 using a polymer gate (photochemical doping) [15]. The mobility at T ¼ 4 K is ab...

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Electronic transport and the localization length in the quantum Hall effect

Cited by 87 publications

References 100 publications

Hopping Conductivity in the Quantum Hall Effect: Revival of Universal Scaling

Hopping Conductivity in the Quantum Hall Effect: Revival of Universal Scaling

Quantum resistance metrology in graphene

Puddle-Induced Resistance Oscillations in the Breakdown of the Graphene Quantum Hall Effect

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