Conservative second-order accurate finite-difference scheme for the coupled Maxwell-Dirac equations

Abstract

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 caonserved within a relative error of order 10−4. 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.