Phase Separation of Edge States in the Integer Quantum Hall Regime

TL;DR

This paper investigates how Coulomb interactions influence edge states in a two-dimensional electron gas under high magnetic fields, revealing phase separation into stripe patterns of different electronic phases.

Contribution

It introduces a self-consistent Schrödinger-Poisson approach to study phase separation of edge states in the integer quantum Hall regime with varying boundary widths.

Findings

Flat bands at the Fermi level form for smooth interfaces.

Phase separation into stripes of compressible and incompressible liquids occurs.

Electrostatic energy minimization leads to stripe formation.

Abstract

Coulomb effects on the edge states of a two dimensional electron gas in the presence of a high magnetic field are studied for different widths of the boundaries. Schr\"odinger and Poisson equations are selfconsistently solved in the integer Quantum Hall regime. Regions of flat bands at the Fermi level appear for smooth interfaces in order to minimize the electrostatic energy related to the existence of dipoles induced by the magnetic field. These plateaus determine the phase separation in stripes of compressible and incompressible electron liquids.