Edge electrostatics revisited

TL;DR

This paper revisits the electrostatics at the edges of a two-dimensional electron gas, improving the modeling by solving the 3D Poisson equation self-consistently and considering many-body and disorder effects.

Contribution

It provides a detailed, self-consistent electrostatic model of quantum Hall edge states, extending previous analytical work and including spin, many-body, and disorder effects.

Findings

Incompressible strips narrower than quantum length scales vanish.

Non-self-consistent models overestimate incompressible strip widths.

Odd integer filling fractions are not stable at high magnetic fields without many-body effects.

Abstract

In this work we investigate in detail, the different regimes of the pioneering work of Chklovskii et al. (1992), which provides an analytical description to model the electrostatics at the edges of a two-dimensional electron gas. We take into account full electrostatics and calculate the charge distribution by solving the 3D Poisson equation self-consistently. The Chklovskii formalism is reintroduced and is employed to determine the widths of the incompressible edge-states also considering the spin degree of freedom. It is shown that, the odd integer filling fractions cannot exist for large magnetic field intervals if many-body effects are neglected. We explicitly show that, the incompressible strips which are narrower than the quantum mechanical length scales vanish. We numerically and analytically show that, the non-self-consistent picture becomes inadequate considering realistic Hall bar geometries, predicting large incompressible strips. The details of this picture is investigated considering device properties together with the many-body and the disorder effects. Moreover, we provide semi-empirical formulas to estimate realistic density distributions for different physical boundary conditions.