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Register a new userDynamical scaling of the quantum Hall plateau transition
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Using different experimental techniques we examine the dynamical scaling of the quantum Hall plateau transition in a frequency range f = 0.1-55 GHz. We present a scheme that allows for a simultaneous scaling analysis of these experiments and all other data in literature. We observe a universal scaling function with an exponent kappa = 0.5 +/- 0.1, yielding a dynamical exponent z = 0.9 +/- 0.2.
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The temperature dependence of the magneto-conductivity in graphene shows that the widths of the longitudinal conductivity peaks, for the N=1 Landau level of electrons and holes, display a power-law behavior following $Delta u propto T^{kappa}$ with a scaling exponent $kappa = 0.37pm0.05$. Similarly the maximum derivative of the quantum Hall plateau transitions $(dsigma_{xy}/d u)^{max}$ scales as $T^{-kappa}$ with a scaling exponent $kappa = 0.41pm0.04$ for both the first and second electron and hole Landau level. These results confirm the universality of a critical scaling exponent. In the zeroth Landau level, however, the width and derivative are essentially temperature independent, which we explain by a temperature independent intrinsic length that obscures the expected universal scaling behavior of the zeroth Landau level.
The quantum Hall plateau transition was studied at temperatures down to 1 mK in a random alloy disordered high mobility two-dimensional electron gas. A perfect power-law scaling with kappa=0.42 was observed from 1.2K down to 12mK. This perfect scaling terminates sharply at a saturation temperature of T_s~10mK. The saturation is identified as a finite-size effect when the quantum phase coherence length (L_{phi} ~ T^{-p/2}) reaches the sample size (W) of millimeter scale. From a size dependent study, T_s propto W^{-1} was observed and p=2 was obtained. The exponent of the localization length, determined directly from the measured kappa and p, is u=2.38, and the dynamic critical exponent z = 1.
We report distinctive magnetotransport properties of a graphene p-n-p junction prepared by controlled diffusion of metallic contacts. In most cases, materials deposited on a graphene surface introduce substantial carrier scattering, which greatly reduces the high mobility of intrinsic graphene. However, we show that an oxide layer only weakly perturbs the carrier transport, which enables fabrication of a high-quality graphene p-n-p junction through a one-step and resist-free method. The measured conductance-gate voltage $(G-V_G)$ curves can be well described by a metal contact model, which confirms the charge density depinning due to the oxide layer. The graphene p-n-p junction samples exhibit pronounced quantum Hall effect, a well-defined transition point of the zeroth Landau level (LL), and scaling behavior. The scaling exponent obtained from the evolution of the zeroth LL width as a function of temperature exhibits a relatively low value of $kappa=0.21pm0.01$. Moreover, we calculate the energy level for the LLs based on the distribution of plateau-plateau transition points, further validating the assignment of the LL index of the QH plateau-plateau transition.
We report quantum Hall experiments on the plateau-insulator transition in a low mobility In_{.53} Ga_{.47} As/InP heterostructure. The data for the longitudinal resistance rho_{xx} follow an exponential law and we extract a critical exponent kappa= .55 pm .05 which is slightly different from the established value kappa = .42 pm .04 for the plateau transitions. Upon correction for inhomogeneity effects, which cause the critical conductance sigma_{xx}^* to depend marginally on temperature, our data indicate that the plateau-plateau and plateau- insulator transitions are in the same universality class.
We study multifractal spectra of critical wave functions at the integer quantum Hall plateau transition using the Chalker-Coddington network model. Our numerical results provide important new constraints which any critical theory for the transition will have to satisfy. We find a non-parabolic multifractal spectrum and we further determine the ratio of boundary to bulk multifractal exponents. Our results rule out an exactly parabolic spectrum that has been the centerpiece in a number of proposals for critical field theories of the transition. In addition, we demonstrate analytically exact parabolicity of related boundary spectra in the 2D chiral orthogonal `Gade-Wegner symmetry class.
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