Dirac方程到一般自旋的格点推广及平带的作用
Lattice generalization of the Dirac equation to general spin and the role of the flat band
摘要：
我们提供了一种新的设置，用于将石墨烯蜂窝晶格中产生的二维赝自旋S=1/2狄拉克方程推广到一般的赝自旋S。我们将这些能带结构设计成包含堆叠三角晶格的最近邻跳跃哈密顿量。我们得到了由二维Dirac方程H=v_FS \cdot p描述的半填充周围的多层低能激发，其中S表示任意自旋S（整数或半整数）。对于整数-S，出现一个平坦的带，其存在定性地修改系统的响应。在物理观测量中，研究了态密度、光电导率和克莱因隧穿特性。我们还研究了陈数以及零能朗道能级简并度。通过改变堆叠模式，拓扑性质显著改变，在多层石墨烯堆叠中没有明显的类似物。
英文摘要：
We provide a novel setup for generalizing the two-dimensional pseudospin S=1/2 Dirac equation, arising in graphene's honeycomb lattice, to general pseudospin-S. We engineer these band structures as a nearest-neighbor hopping Hamiltonian involving stacked triangular lattices. We obtain multi-layered low energy excitations around half-filling described by a two-dimensional Dirac equation of the form H=v_F S\cdot p, where S represents an arbitrary spin-S (integer or half-integer). For integer-S, a flat band appears, whose presence modifies qualitatively the response of the system. Among physical observables, the density of states, the optical conductivity and the peculiarities of Klein tunneling are investigated. We also study Chern numbers as well as the zero-energy Landau level degeneracy. By changing the stacking pattern, the topological properties are altered significantly, with no obvious analogue in multilayer graphene stacks.
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