标题： 拓扑光子Tamm态与Su-Schrieffer-Heeger模型 显示英文标题

标题： Topological Photonic Tamm-States and the Su-Schrieffer-Heeger Model

摘要： 在本文中，我们研究了半无限一维光子晶体与金属界面处拓扑Tamm态的形成。我们表明，当系统处于非平凡拓扑状态时，每个带隙中都有一个Tamm态，而如果系统处于平凡拓扑状态，则带隙中没有Tamm态。我们将Tamm态的消失与从非平凡拓扑系统到平凡拓扑系统的拓扑转变联系起来。这种拓扑转变是由单元格中介电函数的改变驱动的。我们的解释进一步得到了麦克斯韦方程组解与这些解的紧束缚表示存在精确映射的支持。我们表明，基于麦克斯韦方程组的一维光子晶体的紧束缚表示对应于每对带的Su-Schrieffer-Heeger型模型（SSH模型）。在带边附近扩展此表示，我们表明系统可以用类似狄拉克的哈密顿量来描述。这使得可以通过绕数来表征与麦克斯韦方程组解相关的拓扑性质。此外，对于无限系统，我们提供了光子带的解析表达式，从而可以计算出带隙。 显示英文摘要

摘要： In this paper we study the formation of topological Tamm states at the interface between a semi-infinite one-dimensional photonic-crystal and a metal. We show that when the system is topologically non-trivial there is a single Tamm state in each of the band-gaps, whereas if it is topologically trivial the band-gaps host no Tamm states. We connect the disappearance of the Tamm states with a topological transition from a topologically non-trivial system to a topologically trivial one. This topological transition is driven by the modification of the dielectric functions in the unit cell. Our interpretation is further supported by an exact mapping between the solutions of Maxwell's equations and the existence of a tight-binding representation of those solutions. We show that the tight-binding representation of the 1D photonic crystal, based on Maxwell's equations, corresponds to a Su-Schrieffer-Heeger-type model (SSH-model) for each set of pairs of bands. Expanding this representation near the band edge we show that the system can be described by a Dirac-like Hamiltonian. It allows one to characterize the topology associated with the solution of Maxwell's equations via the winding number. In addition, for the infinite system, we provide an analytical expression for the photonic bands from which the band-gaps can be computed.