Reducible Fermi Surface for Multi-layer Quantum Graphs Including Stacked Graphene
Reducible Fermi Surface for Multi-layer Quantum Graphs Including Stacked Graphene
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DOI：
10.1007/s00220-021-04120-z
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发表时间：
2020-05
影响因子：
2.4
通讯作者：
L. Fisher;Wei Li;S. Shipman
中科院分区：
文献类型：
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作者：
L. Fisher;Wei Li;S. Shipman
我们构造了两种类型的多层量子图（度量图上的薛定谔算子），其中波矢和能量的色散函数被证明是单层色散函数中的多项式。这导致代数费米面在任何能量下都可还原为多个分量。每个组件都向图算子的频谱贡献一组频带。当层是石墨烯时，在同一多层结构内允许AA-、AB-和ABC-堆叠。我们介绍的工具之一是外科手术式微积分，用于通过将两个图连接在一起来获得周期量子图的色散函数。费米表面的可还原性允许构造局部缺陷，从而在嵌入辐射连续体的能量处产生束缚态。
We construct two types of multi-layer quantum graphs (Schrödinger operators on metric graphs) for which the dispersion function of wave vector and energy is proved to be a polynomial in the dispersion function of the single layer. This leads to the reducibility of the algebraic Fermi surface, at any energy, into several components. Each component contributes a set of bands to the spectrum of the graph operator. When the layers are graphene, AA-, AB-, and ABC-stacking are allowed within the same multi-layer structure. One of the tools we introduce is a surgery-type calculus for obtaining the dispersion function for a periodic quantum graph by joining two graphs together. Reducibility of the Fermi surface allows for the construction of local defects that engender bound states at energies embedded in the radiation continuum.