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We obtain the solution of the Dirac equation in (2+1) dimensions in thepresence of a constant magnetic field normal to the plane together with atwo-dimensional Dirac-oscillator potential coupling. We study the energyspectrum of graphene quantum dot (QD) defined by electrostatic gates. We givediscussions of our results based on different physical settings, whether thecyclotron frequency is similar or larger/smaller compared to the oscillatorfrequency. This defines an effective magnetic field that produces the effectivequantized Landau levels. We study analytically such field in gate-tunablegraphene QD and show that our structure allow us to control the valleydegeneracy. Finally, we compare our results with already published work andalso discuss the possible applications of such QD.

Gate-Tunable Graphene Quantum Dot and Dirac Oscillator