Dirac费米子的无反射Klein隧穿：Dirac方程分裂算符和交错格子离散的比较
Reflectionless Klein tunneling of Dirac fermions: Comparison of split-operator and staggered-lattice discretization of the Dirac equation
摘要：
无质量狄拉克费米子在电场中沿着场线传播，由于自旋动量锁定和自旋守恒的结合，没有后向散射。这种现象，被称为“克莱因隧道”，可能会丢失，如果狄拉克方程是离散的空间和时间，因为在布里渊区的多个狄拉克锥之间的散射。为了避免这种情况，文献中已经开发了交错时空晶格离散化，在原始正方形晶格的布里渊区中具有单个狄拉克锥。在这里，我们表明，交错的两倍大小的布里渊区，其中实际上包含两个狄拉克锥。我们发现，这种费米子加倍导致一个虚假的崩溃的克莱因隧道，这可以避免一个替代的单锥离散计划的基础上分裂算子的方法。
英文摘要：
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, with one single 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 contains two Dirac 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.
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