Trapping electrons in a circular graphene quantum dot with Gaussian potential

We study the dependence of 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 does 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 but decreases 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.