Transition to Landau Levels in Graphene Quantum Dots

TL;DR

This study explores how magnetic fields influence the electronic states of graphene quantum dots, revealing a transition to Landau levels and highlighting the role of lattice structure and defects in this process.

Contribution

It provides a detailed analysis of the transition to Landau levels in graphene quantum dots, emphasizing the impact of lattice imperfections and chiral-symmetry breaking on level evolution.

Findings

Transition from linear density of states to Landau levels with increasing magnetic field

Level variance variation quantifies K-K' scattering strength

Magnetic field dependence serves as a probe for quantum dot properties

Abstract

We investigate the electronic eigenstates of graphene quantum dots of realistic size (i.e., up to 80 nm diameter) in the presence of a perpendicular magnetic field B. Numerical tight-binding calculations and Coulomb-blockade measurements performed near the Dirac point exhibit the transition from the linear density of states at B=0 to the Landau level regime at high fields. Details of this transition sensitively depend on the underlying graphene lattice structure, bulk defects, and localization effects at the edges. Key to the understanding of the parametric evolution of the levels is the strength of the chiral-symmetry breaking K-K' scattering. We show that the parametric variation of the level variance provides a quantitative measure for this scattering mechanism. We perform measurements of the parametric motion of Coulomb blockade peaks as a function of magnetic field and find good agreement. We thereby demonstrate that the magnetic-field dependence of graphene energy levels may serve as a sensitive indicator for the properties of graphene quantum dots and, in further consequence, for the validity of the Dirac-picture.