Edge of a Half-Filled Landau Level

TL;DR

This study examines the electron occupation at the edge of a quantum Hall droplet at filling factor 1/2, revealing unique scaling behavior and edge properties distinct from odd-denominator states.

Contribution

It provides new insights into the edge structure of half-filled Landau levels using exact diagonalization and composite fermion wavefunctions.

Findings

Edge occupation numbers follow a scaling behavior.

Existence of a well-defined edge at the droplet radius.

Occupation beyond the edge is substantial, unlike odd-denominator states.

Abstract

We have investigated the electron occupation number of the edge of a quantum Hall (QH) droplet at $\nu=1/2$ using exact diagonalization technique and composite fermion trial wavefunction. We find that the electron occupation numbers near the edge obey a scaling behavior. The scaling result indicates the existence of a well-defined edge corresponding to the radius of a compact droplet of uniform filling factor 1/2. We find that the occupation number beyond this edge point is substantial, which is qualitatively different from the case of odd-denominator QH states. We relate these features to the different ways in which composite fermions occupy Landau levels for odd and even denominator states.