Dirac Points for the Honeycomb Lattice with Impenetrable Obstacles
Dirac Points for the Honeycomb Lattice with Impenetrable Obstacles
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DOI：
10.1137/22m1505116
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Wei Li;Junshan Lin;Haifeng Zhang
中科院分区：
文献类型：
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作者：
Wei Li;Junshan Lin;Haifeng Zhang
本文研究了均匀介质中具有不可穿透的周期性障碍物的蜂窝格子的Dirac点。我们考虑了Dirichlet和Neumann特征值问题，并证明了Dirac点的存在性，这两个特征值问题的交叉点的低带表面以及高带表面。此外，我们进行定量分析的特征值和斜率的两个锥形色散表面附近的每个狄拉克点的基础上相结合的层势技术和渐近分析。结果表明，本征值位于蜂窝晶格绿色函数奇异频率附近，色散面斜率与本征值倒数。
This work is concerned with the Dirac points for the honeycomb lattice with impenetrable obstacles arranged periodically in a homogeneous medium. We consider both the Dirichlet and Neumann eigenvalue problems and prove the existence of Dirac points for both eigenvalue problems at crossing of the lower band surfaces as well as higher band surfaces. Furthermore, we perform quantitative analysis for the eigenvalues and the slopes of two conical dispersion surfaces near each Dirac point based on a combination of the layer potential technique and asymptotic analysis. It is shown that the eigenvalues are in the neighborhood of the singular frequencies associated with the Green's function for the honeycomb lattice, and the slopes of the dispersion surfaces are reciprocal to the eigenvalues.