Trapping electrons in a circular graphene quantum dot with Gaussian potential

Abstract

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.