Gate-tunable graphene quantum dot and Dirac oscillator

• The solution of the Dirac equation in (2+1)(2+1) dimensions in the presence of a constant perpendicular magnetic field and the Dirac-oscillator is obtained.
• The energy spectrum of graphene quantum dot (QD) defined by electrostatic gates is analyzed.
• Our results are discussed based on different physical settings, whether the cyclotron frequency is similar or larger/smaller compared to the oscillator frequency.
• The effect of an effective field in gate-tunable graphene QD gave a control of the valley degeneracy.
• Comparison of our results with already published work is done.

We obtain the solution of the Dirac equation in (2+1)(2+1) dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. We study the energy spectrum of graphene quantum dot (QD) defined by electrostatic gates. We give discussions of our results based on different physical settings, whether the cyclotron frequency is similar or larger/smaller compared to the oscillator frequency. This defines an effective magnetic field that produces the effective quantized Landau levels. We study analytically such field in gate-tunable graphene QD and show that our structure allows us to control the valley degeneracy. Finally, we compare our results with already published work and also discuss the possible applications of such QD.