Solving the Fully Coupled Time-Dependent Maxwell-Dirac System: A Second-Order Accurate Numerical Scheme

Owing to their increased carrier velocities, Dirac materials have become a promising option for the integration into nanoelectronics. However, without the aid of simulation software that is able to accurately describe the behavior of these materials, the fabrication of novel devices is extremely challenging. In this work, we present a second-order accurate, multiphysics solution method for the pertinent time-dependent Maxwell-Dirac equations. The numerical stencils of the separate equations are presented, leading to a novel stability criterion for the minimally coupled Dirac equation. Afterwards, the second-order accuracy is demonstrated via a numerical example, in which a Dirac particle is represented as a wave packet.