表面等离激元体系中的狄拉克谱及相关奇异性质的研究

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 Dirac spectra, we will investigate the dipolar and quadruplar modes for various structures including both simple and complex lattices for one- and two-dimensional cases. Our work would offer a better understanding of the physics of Dirac spectra in plasmonic systems.

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。

近十年来，拓扑以不断增长的速度进入物理学。特别的，2016年度的诺贝尔奖颁给三位将拓扑概念引入凝聚态物理学的先驱。本项目负责人受这种思潮的激励，立足于一种特殊的电磁体系—表面等离激元体系，以狄拉克谱作为切入点，研究由此伴随而来的几何位相、拓扑边界态等奇异的物理性质。主要在一维复式格子、二维蜂窝结构中，对于偶极子和多极子进行研究，探讨由狄拉克谱带来的能带反转和边界态。.在项目的执行期间（2014.1-2016.12），我们顺利的完成了以上研究任务。我们系统的研究了一维复式格子的周期石墨烯体系，利用紧束缚模型建立了和电子体系中对应的SSH模型，找到了由具有不同拓扑性质(Zak phase或者绕数)的两种周期结构的界面处的局域态。进一步，我们在人工表面等离激元体系中，构造了类SSH模型的波导，实验测量了拓扑边界态的场分布和局域长度。在这方面，项目负责人以通讯作者身份发表两篇文章：Optics Letters 41, 3698 (2016), Optics Express 23, 21585 (2015)。其中的Opt. Lett.这篇被选为编辑推荐文章。受上述研究的启发，我们还在拓扑绝缘体的电磁散射和环多极子两方面做了一些研究，包括利用拓扑绝缘体的散射测量精细结构常数、增强背散射、反共振，以及金属纳米天线中由环偶极子带来的高品质因子的腔膜和定向散射。在这些方面，负责人以通讯（共同通讯）作者身份发表论文5篇。这些工作为我们开展新的研究工作打下了扎实的基础。