Edge Asymptotics of Planar Electron Densities

TL;DR

This paper investigates the asymptotic behavior of electron densities at the edges of large planar systems in higher Landau levels, revealing step-like structures and boundary characteristics through asymptotic analysis.

Contribution

It provides a detailed asymptotic analysis of edge densities in higher Landau levels, including boundary characteristics for individual and multiple filled levels.

Findings

Density exhibits n distinct steps at the edge in the nth Landau level.

Boundary characteristics are computed in an asymptotic expansion.

Edge behavior differs from bulk due to particle number and magnetic flux correlation.

Abstract

The $N\to\infty$ limit of the edges of finite planar electron densities is discussed for higher Landau levels. For full filling, the particle number is correlated with the magnetic flux, and hence with the boundary location, making the $N\to\infty$ limit more subtle at the edges than in the bulk. In the $n^{\rm th}$ Landau level, the density exhibits $n$ distinct steps at the edge, in both circular and rectangular samples. The boundary characteristics for individual Landau levels, and for successively filled Landau levels, are computed in an asymptotic expansion.