Conservative fourth-order accurate finite-difference scheme to solve the (3+1)D tilted Dirac equation in strained Dirac semimetals
Owing to their increased electron mobility compared to conventional semiconductors, three-dimensional (3D) Dirac semimetals are considered to be promising candidates for integration into next-generation electronic devices. In these materials, the low-energy dynamics of the charge carriers are governed by an effective tilted Dirac equation, in which a mass term appears when strain is applied to […]
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 […]
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 […]