Energy levels of graphene magnetic circular quantum dot

Abdelhadi Belouad,Hocine Bahlouli,Bouchaib Lemaalem,Ahmed Jellal

doi:10.1088/2053-1591/ab6d2f

Abstract

We study the energy levels of graphene magnetic circular quantum dot surrounded by an infinite graphene sheet in the presence of an electrostatic potential. We solve Dirac equation to derive the solutions of energy spectrum associated with different regions composing our system. Using the continuum model and applying boundary conditions at the interface, we obtain analytical results for the energy levels. The dependence of the energy levels on the quantum dot radius, magnetic field and electrostatic potential is analyzed for the two valleys K and . We show that the energy levels exhibit characteristics of interface states and have an energy gap.

Highlights

Graphene has been the subject of massive research throughout the world since the first experiments in 2004 [1, 2] because of its unique electronic properties that could be important for nanoelectronics applications [3–5]
We study the energy levels of graphene magnetic circular quantum dot surrounded by an infinite graphene sheet in the presence of an electrostatic potential
We study the confinement of the charge carriers in a magnetic circular quantum dot in graphene surrounded by an infinite graphene sheet

Summary

Introduction

Graphene has been the subject of massive research throughout the world since the first experiments in 2004 [1, 2] because of its unique electronic properties that could be important for nanoelectronics applications [3–5]. By solving Dirac equation an analytical solution to calculate energy levels and wave functions of mono- and bilayer graphene quantum dots was presented in [27] All these important works are different from the present work but some common features of graphene QD will be pointed out in the conclusion, such as the decrease of the energy band gap as the size of the QD increases. These solutions will be used together with the continuity condition to determine the corresponding energy levels.

Model and theory

Numerical results

Conclusion