论文标题
多层薄膜异质结构的差距标记定理
Gap labeling theorem for multilayer thin film heterostructures
论文作者
论文摘要
准二体系统显示出由于准碘的通用差距结构，这与周期系统中布里鲁因区边界的间隙开口类似。在这些能量差距下方的状态（IDO）的集成密度以少数整数为特征，该整数称为Quasiperiodic Systems的``间隙标记定理'（GLT）（GLT）。在这项研究中，着重于多层薄膜系统，例如扭曲的双层石墨烯和堆叠的过渡金属二核苷，我们使用基于代数称为“非交易性的圆环”的代数的方法扩展了多层系统和层数的多层系统。我们发现，通常以$ n $ layer Systems在$ d $ dimensions中的$ _ {dn} c_d $ integer标签的能量差距和关联的IDO的特征，当准层耦合的效果由Quasiperiodic Intrayodic Intrayodic IntrayerAneer coupling近似。我们证明，通过数值模拟，通用的GLT适用于准膜碘的1D紧密结合模型。
Quasiperiodic systems show a universal gap structure due to quasiperiodicity which is analogous to gap openings at the Brillouin zone boundary in periodic systems. The integrated density of states (IDoS) below those energy gaps are characterized by a few integers, which is known as the ``gap labeling theorem'' (GLT) for quasiperiodic systems. In this study, focusing on multilayer thin film systems such as twisted bilayer graphene and stacked transition metal dichalcogenides, we extend the GLT for multilayer systems of arbitrary dimensions and number of layers, using an approach based on the algebra called ``a noncommutative torus''. We find that the energy gaps and the associated IDoS are generally characterized by $_{DN}C_D$ integer labels in $N$ layer systems in the $D$ dimensions, when the effect of the interlayer coupling can be approximated by a quasiperiodic intralayer coupling for each layer. We demonstrate that the generalized GLT holds for quasiperiodic 1D tight binding models by numerical simulations.
