Super universality of the quantum Hall effect and the "large NN picture" of the ϑ\vartheta angle

It is shown that the "massless chiral edge excitations" are an integral and universal aspect of the low energy dynamics of the $\vartheta$ vacuum that has historically gone unnoticed. Within the $SU(M+N)/S(U(M) \times U(N))$ non-linear sigma model we introduce an effective theory of "edge excitations" that fundamentally explains the quantum Hall effect. In sharp contrast to the common beliefs in the field our results indicate that this macroscopic quantization phenomenon is, in fact, a {\em super universal} strong coupling feature of the $\vartheta$ angle with the replica limit $M=N=0$ only playing a role of secondary importance. To demonstrate super universality we revisit the large $N$ expansion of the $CP^{N-1}$ model. We obtain, for the first time, explicit scaling results for the quantum Hall effect including quantum criticality of the quantum Hall plateau transition. Consequently a scaling diagram is obtained describing the cross-over between the weak coupling "instanton phase" and the strong coupling "quantum Hall phase" of the large $N$ theory. Our results are in accordance with the "instanton picture" of the $\vartheta$ angle but fundamentally invalidate all the ideas, expectations and conjectures that are based on the historical "large $N$ picture."Comment: 40 pages, 9 figure

Quantum criticality, particle-hole symmetry, and duality of the plateau-insulator transition in the quantum Hall regime

We report new experimental data on the plateau-insulator transition in the quantum Hall regime, taken from a low mobility InGaAs/InP heterostructure. By employing the fundamental symmetries of the quantum transport problem we are able to disentangle the universal quantum critical aspects of the magnetoresistance data (critical indices and scaling functions) and the sample dependent aspects due to macroscopic inhomogeneities. Our new results and methodology indicate that the previously established experimental value for the critical index (kappa = 0.42) resulted from an admixture of both universal and sample dependent behavior. A novel, non-Fermi liquid value is found (kappa = 0.57) along with the leading corrections to scaling. The statement of self-duality under the Chern Simons flux attachment transformation is verified.Comment: 4 pages, 2 figure

Evidence for a Quantum Hall Insulator in an InGaAs/InP Heterostructure

We study the quantum critical behavior of the plateau-insulator (PI) transition in a low mobility InGaAs/InP heterostructure. By reversing the direction of the magnetic field (B) we find an averaged Hall resistance \rho_xy which remains quantized at the plateau value h/e^2 throughout the PI transition. We extract a critical exponent \kappa'= 0.57 +/- 0.02 for the PI transition which is slightly different from (and possibly more accurate than) the established value 0.42 +/- 0.04 as previously obtained from the plateau-plateau (PP) transitions.Comment: 3pages, 2 figures; submitted to EP2DS-14 conference proceeding

New Insights into the Plateau-Insulator Transition in the Quantum Hall Regime

We have measured the quantum critical behavior of the plateau-insulator (PI) transition in a low-mobility InGaAs/GaAs quantum well. The longitudinal resistivity measured for two different values of the electron density follows an exponential law, from which we extract critical exponents kappa = 0.54 and 0.58, in good agreement with the value (kappa = 0.57) previously obtained for an InGaAs/InP heterostructure. This provides evidence for a non-Fermi liquid critical exponent. By reversing the direction of the magnetic field we find that the averaged Hall resistance remains quantized at the plateau value h/e^2 through the PI transition. From the deviations of the Hall resistance from the quantized value, we obtain the corrections to scaling.Comment: accepted proceedings of EP2DS-15 (to be published in Physica E

The effect of carrier density gradients on magnetotransport data measured in Hall bar geometry

We have measured magnetotransport of the two-dimensional electron gas in a Hall bar geometry in the presence of small carrier density gradients. We find that the longitudinal resistances measured at both sides of the Hall bar interchange by reversing the polarity of the magnetic field. We offer a simple explanation for this effect and discuss implications for extracting conductivity flow diagrams of the integer quantum Hall effect.Comment: 7 pages, 8 figure

The effects of macroscopic inhomogeneities on the magneto transport properties of the electron gas in two dimensions

In experiments on electron transport the macroscopic inhomogeneities in the sample play a fundamental role. In this paper and a subsequent one we introduce and develop a general formalism that captures the principal features of sample inhomogeneities (density gradients, contact misalignments) in the magneto resistance data taken from low mobility heterostructures. We present detailed assessments and experimental investigations of the different regimes of physical interest, notably the regime of semiclassical transport at weak magnetic fields, the plateau-plateau transitions as well as the plateau-insulator transition that generally occurs at much stronger values of the external field only. It is shown that the semiclassical regime at weak fields plays an integral role in the general understanding of the experiments on the quantum Hall regime. The results of this paper clearly indicate that the plateau-plateau transitions, unlike the the plateau-insulator transition, are fundamentally affected by the presence of sample inhomogeneities. We propose a universal scaling result for the magneto resistance parameters. This result facilitates, amongst many other things, a detailed understanding of the difficulties associated with the experimental methodology of H.P. Wei et.al in extracting the quantum critical behavior of the electron gas from the transport measurements conducted on the plateau-plateau transitions.Comment: 20 pages, 9 figure

Theta renormalization, electron-electron interactions and super universality in the quantum Hall regime

The renormalization theory of the quantum Hall effect relies primarily on the non-perturbative concept of theta renormalization by instantons. Within the generalized non-linear sigma model approach initiated by Finkelstein we obtain the physical observables of the interacting electron gas, formulate the general (topological) principles by which the Hall conductance is robustly quantized and derive - for the first time - explicit expressions for the non-perturbative (instanton) contributions to the renormalization group beta- and gamma- functions. Our results are in complete agreement with the recently proposed idea of super universality which says that the fundamental aspects of the quantum Hall effect are all generic features the instanton vacuum concept in asymptotically free field theory.Comment: ReVTeX, 38 pages, 9 figure

Universal flow diagram for the magnetoconductance in disordered GaAs layers

The temperature driven flow lines of the diagonal and Hall magnetoconductance data (G_{xx},G_{xy}) are studied in heavily Si-doped, disordered GaAs layers with different thicknesses. The flow lines are quantitatively well described by a recent universal scaling theory developed for the case of duality symmetry. The separatrix G_{xy}=1 (in units e^2/h) separates an insulating state from a spin-degenerate quantum Hall effect (QHE) state. The merging into the insulator or the QHE state at low temperatures happens along a semicircle separatrix G_{xx}^2+(G_{xy}-1)^2=1 which is divided by an unstable fixed point at (G_{xx},G_{xy})=(1,1).Comment: 10 pages, 5 figures, submitted to Phys. Rev. Let