Electrical transport properties of bidimensional electron liquids in the presence of a high magnetic field

TL;DR

This thesis develops a hydrodynamical model for edge excitations in quantum Hall systems, deriving the chiral Luttinger liquid from fundamental principles and analyzing conductance corrections due to tunneling.

Contribution

It introduces a derivation of the chiral Luttinger liquid model from coarse-graining and Landau level projection, providing a new theoretical foundation for edge state dynamics.

Findings

Recovered ideal Hall conductance in the absence of tunneling

Derived expressions for conductance corrections with tunneling

Compared results with recent experiments and existing models

Abstract

In this thesis we derive a hydrodynamical model to describe the dynamics of density excitations localized at the edges of a Quantum Hall bar. In particular we show that the chiral Luttinger liquid model for the edges excitations can be derived from the coarse-graining and a lowest Landau level projection procedure without reference to the Quantum Hall effect. We use this model to calculate the Landauer-Buettiker conductances in generic experimental setups. In the absence of tunneling the ideal Hall conductance is recovered. When the tunneling between the edges is explicitely taken into account we obtain expressions for the corrections to the ideal conductance. We discuss our result vis-a-vis recent experiments in the weak tunneling regime and previous theoretical models.