The Structure of Fractional Edge States: A Composite Fermion Approach

TL;DR

This paper investigates the structure of fractional quantum Hall edge states using a composite fermion approach, revealing how edge sharpness influences electron density and the emergence of fractional channels.

Contribution

It introduces a numerical Hartree approximation method to analyze edge structures for various filling factors, highlighting the transition from electron to fractional channels as edge sharpness varies.

Findings

For sharp edges, the one-electron picture holds.

Increasing edge width introduces fractional channels.

Number of channels scales as the square root of edge width.

Abstract

I study the structure of the two-dimensional electron gas edge in the quantum Hall regime using the composite fermion approach. The electron density distribution and the composite fermion energy spectrum are obtained numerically in Hartree approximation for bulk filling factors $\nu=1,1/3,2/3,1/5$. For a very sharp edge of the $\nu=1$ state the one-electron picture is valid. As the edge width $a$ is increased the density distribution shows features related to the fractional states and new fractional channels appear in pairs. For a very smooth edge I find quasiclassically the number of channels $p\sim\sqrt{a/l_H}$, where $l_H$ is the magnetic length.