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Register a new userGravity Dual of a Quantum Hall Plateau Transition
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We show how to model the transition between distinct quantum Hall plateaus in terms of D-branes in string theory. A low energy theory of 2+1 dimensional fermions is obtained by considering the D3-D7 system, and the plateau transition corresponds to moving the branes through one another. We study the transition at strong coupling using gauge/gravity duality and the probe approximation. Strong coupling leads to a novel kind of plateau transition: at low temperatures the transition remains discontinuous due to the effects of dynamical symmetry breaking and mass generation, and at high temperatures is only partially smoothed out.
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Recent high-precision results for the critical exponent of the localization length at the integer quantum Hall (IQH) transition differ considerably between experimental ($ u_text{exp} approx 2.38$) and numerical ($ u_text{CC} approx 2.6$) values obtained in simulations of the Chalker-Coddington (CC) network model. We revisit the arguments leading to the CC model and consider a more general network with geometric (structural) disorder. Numerical simulations of this new model lead to the value $ u approx 2.37$ in very close agreement with experiments. We argue that in a continuum limit the geometrically disordered model maps to the free Dirac fermion coupled to various random potentials (similar to the CC model) but also to quenched two-dimensional quantum gravity. This explains the possible reason for the considerable difference between critical exponents for the CC model and the geometrically disordered model and may shed more light on the analytical theory of the IQH transition. We extend our results to network models in other symmetry classes.
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 thermoelectric Hall effect is the generation of a transverse heat current upon applying an electric field in the presence of a magnetic field. Here we demonstrate that the thermoelectric Hall conductivity $alpha_{xy}$ in the three-dimensional Dirac semimetal ZrTe$_5$ acquires a robust plateau in the extreme quantum limit of magnetic field. The plateau value is independent of the field strength, disorder strength, carrier concentration, or carrier sign. We explain this plateau theoretically and show that it is a unique signature of three-dimensional Dirac or Weyl electrons in the extreme quantum limit. We further find that other thermoelectric coefficients, such as the thermopower and Nernst coefficient, are greatly enhanced over their zero-field values even at relatively low fields.
We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.
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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