We study how the trapping time of an electron in a circular graphene quantum dot depends on the electron’s angular momentum and on the parameters of the external Gaussian potential used to induce the dot. The trapping times are calculated through a numerical determination of the quasi-bound states of electron from the two-dimensional Dirac-Weyl equation. It is shown that on increasing the angular momentum, not only the trapping time decreases but also the trend of how the trapping time depends on the effective radius of the dot changes. | Communications in Physics, Vol. 28, No. 1 (2018), pp. 51-60 DOI: TRAPPING ELECTRONS IN A CIRCULAR GRAPHENE QUANTUM DOT WITH GAUSSIAN POTENTIAL NHUNG T. T. NGUYEN † Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Ba Dinh, Hanoi, Vietnam † E-mail: ntnhung@ Received 16 January 2018 Accepted for publication 12 March 2018 Published 26 March 2018 Abstract. We study how the trapping time of an electron in a circular graphene quantum dot depends on the electron’s angular momentum and on the parameters of the external Gaussian potential used to induce the dot. The trapping times are calculated through a numerical determination of the quasi-bound states of electron from the two-dimensional Dirac-Weyl equation. It is shown that on increasing the angular momentum, not only the trapping time decreases but also the trend of how the trapping time depends on the effective radius of the dot changes. In particular, as the dot radius increases, the trapping time increases for m 3. The trapping time however always decreases upon increasing the potential height. It is also found that the wave functions corresponding to the states of larger trapping times or higher m are more localized in space. Keywords: quasi-bound state, localization, trapping time. Classification numbers: , .−b, . c 2018 Vietnam Academy of Science and Technology 52 NHUNG T. T. NGUYEN I. INTRODUCTION Graphene is a two-dimensional conducting material made up from a single layer of carbon atoms with unique electronic properties [1]. Due to the special sublattice symmetry of graphene, electrons in graphene under low energy excitations can be considered as quasi-relativistic massless chiral fermions, which are formally described by the Dirac-Weyl equation. Anomalous Hall effect [2], absence of backscattering and Klein paradox [3] are examples of the most intriguing properties possessed by the quasi-relativistic .
