论文标题
具有坚不可摧的障碍物的蜂窝晶格的狄拉克点
Dirac points for the honeycomb lattice with impenetrable obstacles
论文作者
论文摘要
这项工作与蜂窝状晶格的狄拉克点有关，并在均匀介质中定期排列不可穿透的障碍物。我们考虑了Dirichlet和Neumann特征值问题，并证明了在较低频段表面的交叉以及更高的频带表面时的特征值问题的存在。此外，我们基于层电位技术和渐近分析的组合，对每个越野点附近的特征值和两个圆锥分散表面的斜率进行定量分析。结果表明，特征值位于与蜂蜜晶格的绿色功能相关的奇异频率附近，并且分散表面的斜率与特征值相处。
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.
