表面等离激元体系中的狄拉克谱及相关奇异性质的研究

项目名称： 表面等离激元体系中的狄拉克谱及相关奇异性质的研究

项目编号： No.11304038

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 韩德专

作者单位： 重庆大学

项目金额： 25万元

中文摘要： 最近，狄拉克谱在电磁波中的诸多奇异性质获得国际学术界的关注。由于狄拉克方程所刻画的旋量场的本质，导致了边界态、拓扑元激发以及其他独特的传播行为。在一维链、类石墨烯的表面等离激元体系中，我们发现了狄拉克谱的存在，并初步研究了能带结构、边界态的特殊性质。但是，若要系统地建立与电子体系对应的狄拉克哈密顿量，还有一些非常重要的问题有待解决。例如，如何找到与质量项相关的能带反转、拓扑元激发、贝利位相？如何完善狄拉克哈密顿量对任意矢量场的边界态行为的描述？本项目拟研究这些重要的科学问题，首先基于严格的多重散射理论，验证准静态近似、紧束缚近似的成立条件，建立表面等离激元与电子体系的对应；利用这些模型，系统研究一维单、复式格子，二维三角、蜂窝结构，电偶、四极子，等各种情况下狄拉克谱的相关性质，探索可能与之伴随的拓扑元激发、贝利位相等，深化和完善对表面等离激元系统的认识。

中文关键词： 表面等离激元；狄拉克谱；几何位相；拓扑光子学；能带结构

英文摘要： Dirac spectra in the electromagnetic systems have received considerable attention in recent years. Special edge states, topological excitations, and unique transport behaviors due to the features of the spinor described by the Dirac equation, are observed both theoretically and experimentally. In one-dimensional chains and two-dimensional honeycomb plasmonic systems, we have identified existence of Dirac spectra, and studied corresponding band structures and edge states which exhibit interesting characteristics. However, in order to achieve the analogs of Dirac Hamiltonian in electronic systems, some fundamental questions still remain unresolved. For instance, how to identify the existence of band inversion, topological excitations, and Berry phase induced by the mass term in Dirac equation? Another important issue is how to predict edge states for arbitrary vector fields by applying proper boundary conditions of Dirac equation. In this proposal, we will tackle these important issues. Based on the multiple-scattering theory, we will examine the validity of the quasi-static approximation, and tight-binding model, and further construct the possible mapping between plasmonics and electronics. In order to explore the novel properties such as boundary conditions, topological excitations, and Berry phase related to Di

英文关键词： surface plasmon polariton；Dirac spectrum；Berry phase；topological photonics；band structure