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arXiv 2005.05680cond-mat.mes-hallphysics.app-ph
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基于拓扑开口环谐振器的$\cal PT$对称性依赖于增益和损耗的超材料

Topological split-ring resonator based metamaterials with $\cal PT$ symmetry relying on gain and loss

N. Lazarides, G. P. Tsironis

摘要:

介绍了一种依赖于平衡增益和损耗的具有奇偶时间(${\cal PT}$)对称性的一维超材料,其包括磁耦合开口环谐振器(SRR)。一个特殊的拓扑结构,结合了一个平凡的(拓扑)二聚体配置与平凡的(非拓扑)二聚体配置,其中分离的中央SRR既没有增益或损失,进行了研究。通过对这种拓扑${\cal PT}$超材料(PTMM)的动力学方面的关注,数值证明了在中心SRR处存在{ \em拓扑保护界面态}.相应的{ \em二次特征值问题}的求解表明,保护状态实际上是拓扑PTMM的一个鲁棒本征模,其特征值孤立于两带频谱的间隙中间(中间间隙状态).直接数值模拟已被进一步用于确定这些状态的鲁棒性和动态稳定性的参数空间中的{ \em二聚强度}和{ \em增益-损失系数}。

英文摘要:

A one-dimensional metamaterial with parity-time (${\cal PT}$) symmetry that relies on balanced gain and loss is introduced, comprising of magnetically coupled split-ring resonators (SRRs). A particular topology that combines a non-trivial (topological) dimer configuration with a trivial (non-topological) dimer configuration which are separated by a central SRR with neither gain or loss, is investigated. By focusing on the dynamical aspects of such a topological ${\cal PT}$ metamaterial (PTMM), the existence of {\em topologically protected interface states} which are localized at the central SRR is demonstrated numerically. The solution of the corresponding {\em quadratic eigenvalue problem} reveals that the protected state is actually a robust eigenmode of the topological PTMM, whose eigenvalue is isolated in the middle of the gap (mid-gap state) of the two-band frequency spectrum. Direct numerical simulations have been further used to determine the robustness and dynamic stability of these states in the parameter space of the {\em dimerization strength} and the {\em gain-loss coefficient}.

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