States near Dirac points of rectangular graphene dot in a magnetic field

TL;DR

This paper explores the unique electronic states near the Dirac points in rectangular graphene dots under a magnetic field, revealing tunable quasi-degenerate levels and edge-localized wavefunctions.

Contribution

It uncovers the formation of a quasi-degenerate level near zero energy and provides a scaling relation for magnetic field-dependent states in large graphene dots.

Findings

A quasi-degenerate level forms near zero energy.

Number of states in this level can be tuned by magnetic field.

Wavefunctions are localized on zigzag edges, with some being field-independent.

Abstract

In neutral graphene dots the Fermi level coincides with the Dirac points. We have investigated in the presence of a magnetic field several unusual properties of single electron states near the Fermi level of such a rectangular-shaped graphene dot with two zigzag and two armchair edges. We find that a quasi-degenerate level forms near zero energy and the number of states in this level can be tuned by the magnetic field. The wavefunctions of states in this level are all peaked on the zigzag edges with or without some weight inside the dot. Some of these states are magnetic field-independent surface states while the others are field-dependent. We have found a scaling result from which the number of magnetic field-dependent states of large dots can be inferred from those of smaller dots.