The dynamics of low energy charge carriers in a graphene quantum dot subjected to a time-dependent local field is investigated numerically. In particular, we study a configuration where a Coulomb electric field is provided by an ion traversing the graphene sample. A Galerkin-like numerical scheme is introduced to solve the massless Dirac equation describing charge carriers subjected to space- and time-dependent electromagnetic potentials and is used to evaluate the field induced interband transitions. It is demonstrated that as the ion goes through graphene, electron-hole pairs are generated dynamically via the adiabatic pair creation mechanism around avoided crossings, similar to electron-positron pair generation in low energy heavy ion collisions.
@article{arxiv.2009.07648,
title = {Plunging in the Dirac sea using graphene quantum dots},
author = {F. Fillion-Gourdeau and P. Levesque and S. MacLean},
journal= {arXiv preprint arXiv:2009.07648},
year = {2020}
}