The effect of inter-edge Coulomb interactions on the transport between quantum Hall edge states

In a recent experiment, Milliken {\em et al.} demonstrated possible evidence for a Luttinger liquid through measurements of the tunneling conductance between edge states in the $\nu=1/3$ quantum Hall plateau. However, at low temperatures, a discrepancy exists between the theoretical predictions based on Luttinger liquid theory and experiment. We consider the possibility that this is due to long-range Coulomb interactions which become dominant at low temperatures. Using renormalization group methods, we calculate the cross-over behaviour from Luttinger liquid to the Coulomb interaction dominated regime. The cross-over behaviour thus obtained seems to resolve one of the discrepancies, yielding good agreement with experiment.Comment: 4 pages, RevTex, 2 postscript figures, tex file and figures have been uuencode

Simulation of resonant tunneling heterostructures: numerical comparison of a complete Schr{ö}dinger-Poisson system and a reduced nonlinear model

Two different models are compared for the simulation of the transverse electronic transport through an heterostructure: a $1D$ self-consistent Schr{ö}dinger-Poisson model with a numerically heavy treatment of resonant states and a reduced model derived from an accurate asymptotic nonlinear analysis. After checking the agreement at the qualitative and quantitative level on quite well understood bifurcation diagrams, the reduced model is used to tune double well configurations for which nonlinearly interacting resonant states actually occur in the complete self-consistent model

Determination of the electron density in GaAs/AlxGa1-xAs heterostructures

An optimized self-consistent method for determination of the quantal electron density is presented. It is applied, in the zero-temperature case, to devices with either partial or full donor ionization. A Thomas-Fermi approximation for the T=0 limit is developed and shown to be appropriate for systematic studies of the two-dimensional electron density, σ − . A suitable linear approximation is found that provides simple and accurate analytic expressions for σ − in terms of the physical parameters of the device