Edge and bulk components of lowest-Landau-level orbitals, correlated fractional quantum Hall effect incompressible states, and insulating behavior in finite graphene samples

TL;DR

This paper investigates the interplay of edge and bulk states in finite graphene under strong magnetic fields, revealing fractional quantum Hall states, insulating gaps, and edge effects through many-body calculations.

Contribution

It introduces a detailed analysis of edge and bulk components in fractional quantum Hall states in finite graphene using exact diagonalization with zigzag boundary conditions.

Findings

Fractional quantum Hall states occur at specific angular momenta.

An insulating gap opens at the Dirac point, increasing with magnetic field.

Bulk electron density depletion affects excitation energies and edge charge accumulation.

Abstract

Many-body calculations of the total energy of interacting Dirac electrons in finite graphene samples exhibit joint occurrence of cusps at angular momenta corresponding to fractional fillings characteristic of formation of incompressible (gapped) correlated states (nu=1/3 in particular) and opening of an insulating energy gap (that increases with the magnetic field) at the Dirac point, in correspondence with experiments. Single-particle basis functions obeying the zigzag boundary condition at the sample edge are employed in exact diagonalization of the interelectron Coulomb interaction, showing, at all sizes, mixed equal-weight bulk and edge components. The consequent depletion of the bulk electron density attenuates the fractional-quantum-Hall-effect excitation energies and the edge charge accumulation results in a gap in the many-body spectrum.