Institut für Physik, Karl-Franzens-Universität Graz, Universitätsplatz 5, 8010 Graz, Austria.
Phys Rev E. 2017 Nov;96(5-1):053312. doi: 10.1103/PhysRevE.96.053312. Epub 2017 Nov 27.
A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.
针对存在一般电磁织构的（2+1）-维狄拉克方程，开发了一种单锥有限差分格方案。后者在（2+1）-维交错网格上使用二阶精度的有限差分方案表示。通过对波函数进行佩尔尔斯-施温格替换，将电磁（矢量）势引入狄拉克方程。由此，单锥能量色散和规范不变性从连续体传递到格构公式。通过与零矢量势的方案进行比较，确定了形式方案的守恒定律和稳定性特性。通过与矢量势的一致性，推断出磁化项的位置。基于这个形式方案，提出并测试了几种数值方案。针对面内磁化存在情况下的单费米子输运，给出了几个基本示例，使用了拓扑绝缘体表面的典型材料参数。
