Scaling flow diagram in the fractional quantum Hall regime of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>GaAs</mml:mi><mml:mo>∕</mml:mo><mml:msub><mml:mi>Al</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi>Ga</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mi>As</mml:mi></mml:mrow></mml:math>heterostructures

Murzin, S. S.; Дорожкин, С. И.; Maude, D. K.; Jansen, A. G. M.

doi:10.1103/physrevb.72.195317

Cited by 23 publications

(43 citation statements)

References 33 publications

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“…The N-shaped features can be described by the density-dependent s xx (n) and s xy (n) obtained from the so-called semicircle relation (see Ruzin & Feng (1995) and references therein). This relation, which is also rooted in the complex-variable interpretation of magneto-transport, is known to work well in GaAs-based 2DESs, both in the integer and in the fractional QHE regimes (Shahar et al 1997;Murzin et al 2002Murzin et al , 2005. For a plateau-to-plateau transition between incompressible filling factors n 1 < n 2 , the semicircle relation gives s 2 xx = (s xy − n 1 )(n 2 − s xy ) (in units of e 2 /h).…”

Section: Extracting the Longitudinal And Transverse Conductivity Frommentioning

confidence: 77%

Fractional quantum Hall effect in suspended graphene probed with two-terminal measurements

Skachko

Duerr

et al. 2010

Phil. Trans. R. Soc. A.

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Recently, fractional quantization of two-terminal conductance was reported in suspended graphene. The quantization, which was clearly visible in fields as low as 2 T and persistent up to 20 K in 12 T, was attributed to the formation of an incompressible fractional quantum Hall state. Here, we argue that the failure of earlier experiments to detect the integer and fractional quantum Hall effect with a Hall-bar lead geometry is a consequence of the invasive character of voltage probes in mesoscopic samples, which are easily shorted out owing to the formation of hot spots near the edges of the sample. This conclusion is supported by a detailed comparison with a solvable transport model. We also consider, and rule out, an alternative interpretation of the quantization in terms of the formation of a p-n-p junction, which could result from contact doping or density inhomogeneity. Finally, we discuss the estimate of the quasi-particle gap of the quantum Hall state. The gap value, obtained from the transport data using a conformal mapping technique, is considerably larger than in GaAs-based two-dimensional electron systems, reflecting the stronger Coulomb interactions in graphene.

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Section: Extracting the Longitudinal And Transverse Conductivity Frommentioning

confidence: 77%

Fractional quantum Hall effect in suspended graphene probed with two-terminal measurements

Skachko

Duerr

et al. 2010

Phil. Trans. R. Soc. A.

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“…With this data we compute IR initial conditions from (B. 16 . At the end we check by plotting that the asymptotics indeed are as expected (see Fig.…”

Section: B21 Numerical Strategymentioning

confidence: 99%

A holographic model for the fractional quantum Hall effect

Lippert

Meyer

Taliotis

2015

J. High Energ. Phys.

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Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a Γ 0 (2) modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an SL(2, Z)-invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: we specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the SL(2, Z) action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.

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“…We expect that in experimental situations the quantization of Hall conductivity should be more prominent. In conventional quantum Hall systems, recent experiments [27] explored the temperature driven We note that even for states out of the original surface gap, which were metallic in the clean limit, ( xx , xy ) scales to the fixed points (0, AE1=2). This means that all the surface states are localized, while a transverse current flows.…”

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confidence: 99%

Surface-Quantized Anomalous Hall Current and the Magnetoelectric Effect in Magnetically Disordered Topological Insulators

2011

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Quantum anomalous Hall (QAH) effect in magnetic topological insulator (TI) is a novel transport phenomenon in which the Hall resistance reaches the quantum plateau in the absence of external magnetic field 1-3. Recently, this exotic effect has been discovered experimentally in an ultrathin film of the Bi 2 Te 3 family TI with spontaneous ferromagnetic (FM) order 3-6. An important question concerning the QAH state is whether it is simply a zero-magnetic-field version of the quantum Hall (QH) effect, or if there is new physics beyond the conventional paradigm. Here we report experimental investigations on the quantum phase transition between the two opposite Hall plateaus of a QAH insulator caused by magnetization reversal. We observe a well-defined plateau with zero Hall conductivity over a range of magnetic field around coercivity, consistent with a recent theoretical prediction 7. The features of the zero Hall plateau are shown to be closely related to that of the QAH effect, but its temperature evolution exhibits quantitative differences from the network model for conventional QH plateau transition 8. We propose that the chiral edge states residing at the magnetic domain boundaries, which are unique to a QAH insulator, are responsible for the zero Hall plateau. The rich magnetic domain dynamics makes the QAH effect a distinctive class of quantum phenomenon that may find novel applications in spintronics. The realization of QAH effect requires that a two-dimensional (2D) material must be FM, topological, and insulating simultaneously 9. Magnetically doped TIs have been proposed 1, 2, 10-12 and experimentally proved 3-6 to be an ideal material system for fulfilling these stringent requirements. For a 3D TI, the inverted bulk band structure ensures topologically protected metallic surface states (SSs), which become 2D when the film is sufficiently thin 13. The spontaneous FM order induced by magnetic doping not only leads to the anomalous Hall effect, but also opens an energy gap at the Dirac point. When the Fermi level (E F) lies within this gap, the only remaining conduction channel is the quasi-one-dimensional chiral edge state, which gives rise to quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field 3, 14. Up to date, the QAH effect has been observed in Cr or V doped (Bi,Sb) 2 Te 3 TI thin films with accurately controlled chemical composition and thickness grown by molecular beam epitaxy (MBE) 3-6. The MBE-grown QAH insulator film studied here has a chemical formula Cr 0.23 (Bi 0.4 Sb 0.6) 1.77 Te 3 and thickness d = 5 QL (quintuple layer). Shown in Fig. 1a is a schematic drawing of the transport device, which is similar to that reported previously 3. The film is manually scratched into a Hall bar geometry, and the SrTiO 3 substrate is used as the bottom gate oxide due to its large dielectric constant at low temperature. The Cr concentration, hence the density of local moment, is higher than that in the sample where the QAH effect was originally discovered 3. As a result, the...

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Scaling flow diagram in the fractional quantum Hall regime ofGaAs∕AlxGa1−xAsheterostructures

Cited by 23 publications

References 33 publications

Fractional quantum Hall effect in suspended graphene probed with two-terminal measurements

Fractional quantum Hall effect in suspended graphene probed with two-terminal measurements

A holographic model for the fractional quantum Hall effect

Surface-Quantized Anomalous Hall Current and the Magnetoelectric Effect in Magnetically Disordered Topological Insulators

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