21 research outputs found
Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar
The 2-- to 1--dimensional crossover of the localisation length of electrons
confined to a disordered quantum wire of finite width is studied in a
model of electrons moving in the potential of uncorrelated impurities. An
analytical formula for the localisation length is derived, describing the
dimensional crossover as function of width , conductance and
perpendicular magnetic field . On the basis of these results, the scaling
analysis of the quantum Hall effect in high Landau levels, and the
delocalisation transition in a quantum Hall wire are reconsidered.Comment: 12 pages, 7 figure
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