Plunging in the Dirac sea using graphene quantum dots

Abstract

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-type numerical scheme is introduced to solve the massless Dirac equation describing charge carriers subjected to space- A nd 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.