Perfectly matched layers for the Dirac equation in general electromagnetic texture.

Abstract

Perfectly matched layer (PML) boundary conditions are constructed for the Dirac equation and general electromagnetic potentials. A PML extension is performed for the partial differential equation and two versions of a staggered-grid single-cone finite-difference scheme. For the latter, PML auxiliary functions are computed either within a Crank-Nicholson scheme or one derived from the formal continuum solution in integral form. Stability conditions are found to be more stringent than for the original scheme. Spectral properties under spatially uniform PML confirm damping of any out-propagating wave contributions. Numerical tests deal with static and time-dependent electromagnetic textures in the boundary regions for parameters characteristic for topological insulator surfaces. When compared to the alternative imaginary-potential method, PML offers vastly improved wave absorption owing to a more efficient suppression of back-reflection. Remarkably, this holds for time-dependent textures as well, making PML a useful approach for transient transport simulations of Dirac fermion systems.