Donís Vela A, Lemut G, Pacholski M J, Tworzydło J, Beenakker C W J
Instituut-Lorentz, Universiteit Leiden, PO Box 9506, RA Leiden, 2300, The Netherlands.
Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warszawa, Poland.
J Phys Condens Matter. 2022 Jul 7;34(36). doi: 10.1088/1361-648X/ac7d2d.
Massless Dirac fermions in an electric field propagate along the field lines without backscattering, due to the combination of spin-momentum locking and spin conservation. This phenomenon, known as 'Klein tunneling', may be lost if the Dirac equation is discretized in space and time, because of scattering between multiple Dirac cones in the Brillouin zone. To avoid this, a staggered space-time lattice discretization has been developed in the literature, withsingle Dirac cone in the Brillouin zone of the original square lattice. Here we show that the staggering doubles the size of the Brillouin zone, which actually containsDirac cones. We find that this fermion doubling causes a spurious breakdown of Klein tunneling, which can be avoided by an alternative single-cone discretization scheme based on a split-operator approach.
由于自旋 - 动量锁定和自旋守恒的结合，无质量狄拉克费米子在电场中沿电场线传播且无背散射。这种现象被称为“克莱因隧穿”，如果狄拉克方程在空间和时间上离散化，由于布里渊区中多个狄拉克锥之间的散射，这种现象可能会消失。为避免这种情况，文献中已开发出一种交错时空晶格离散化方法，在原始正方形晶格的布里渊区中有单个狄拉克锥。在此我们表明，交错使布里渊区的大小翻倍，而该布里渊区实际上包含狄拉克锥。我们发现这种费米子翻倍会导致克莱因隧穿的虚假崩溃，这可以通过基于分裂算符方法的另一种单锥离散化方案来避免。
