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.

Reflectionless Klein tunneling of Dirac fermions: comparison of split-operator and staggered-lattice discretization of the Dirac equation

“…One method works in real space on a staggered space-time lattice [7,8], the other method works in Fourier space using a split-operator technique [9]. The staggered-lattice discretization is due to Hammer, Pötz, and Arnold (HPA) [7,8], and has been applied to a variety of problems in condensed matter physics [10][11][12][13]. For free fermions (V, A ≡ 0) it has the bandstructure sin 2…”

A Miniaturized Anechoic Chamber: Omnidirectional Impedance Matching Based on Truncated Spatial Kramers–Kronig Medium

“…[1,2] Capable of absorbing arbitrarily incident electromagnetic (EM) waves, PMLs have been widely used in open-boundary problems to truncate infinite computational domains to finite ones. [3][4][5] However, physical implementation of PMLs has been elusive so far, due to challenges to realize the complex constitutive tensors using real structures. In microwave engineering, PMLs are often replaced by different kinds of absorbers, such as pyramidal absorber, and multilayer dielectric absorber.…”