72 research outputs found
Super universality of the quantum Hall effect and the "large picture" of the angle
It is shown that the "massless chiral edge excitations" are an integral and
universal aspect of the low energy dynamics of the vacuum that has
historically gone unnoticed. Within the
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 angle with the replica limit only playing a
role of secondary importance. To demonstrate super universality we revisit the
large expansion of the 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
theory. Our results are in accordance with the "instanton picture" of the
angle but fundamentally invalidate all the ideas, expectations and
conjectures that are based on the historical "large 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
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