Proposal for a magnetic field induced graphene dot

TL;DR

This paper investigates magnetic field-induced quantum dots in graphene, revealing unique confinement properties and energy spectra through numerical analysis, and introduces the concept of an antidot with reversed potential sign.

Contribution

It presents a novel model for magnetic field-induced graphene quantum dots and demonstrates their unique energy confinement characteristics through numerical calculations.

Findings

Quantum dots are confined between Landau levels 0 and -1.

Reversing the potential sign creates an antidot confining electrons between Landau levels 0 and +1.

The energy spectrum confirms the unique confinement behavior in graphene quantum dots.

Abstract

Quantum dots induced by a strong magnetic field applied to a single layer of graphene in the perpendicular direction are investigated. The dot is defined by a model potential which consists of a well of depth $\Delta V$ relative to a flat asymptotic part and quantum states formed from the zeroth Landau level are considered. The energy of the dot states cannot be lower than $-\Delta V$ relative to the asymptotic potential. Consequently, when $\Delta V$ is chosen to be about half of the gap between the zeroth and first Landau levels, the dot states are isolated energetically in the gap between Landau level 0 and Landau level -1. This is confirmed with numerical calculations of the magnetic field dependent energy spectrum and the quantum states. Remarkably, an antidot formed by reversing the sign of $\Delta V$ also confines electrons but in the energy region between Landau level 0 and Landau level +1. This unusual behaviour gives an unambiguous signal of the novel physics of graphene quantum dots.