Conservative Second-Order Accurate Finite-Difference Scheme for the Coupled Maxwell-Dirac Equations

The recent development of nanoelectronic devices that incorporate Dirac materials has highly increased the need for adequate simulation and modelling tools. This paper introduces an accurate, multiphysics finite-difference time-domain method to solve the pertinent Maxwell-Dirac equations. The stability criterion for the Dirac equation with electromagnetic fields is derived, which reduces to the Courant-Friedrichs-Lewy condition in the absence of electromagnetic fields. Validation examples show the second-order accuracy of the novel fully coupled Maxwell-Dirac scheme and illustrate that total norm and energy are conserved within a relative error of order 1e-4. The method is applied to a ZrTe5 waveguide and it is found that even at low field strengths, the charge carriers can be accelerated to 80% of the Fermi velocity. Furthermore, the flexibility of the advocated method allows for the seamless integration into existing computational electromagnetics frameworks and the possible extension to higher-order schemes.