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arXiv 2201.05456physics.opticscond-mat.mes-hall
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一维光子晶体拓扑模的Wannier函数方法

Wannier Function Methods for Topological Modes in 1D Photonic Crystals

Vaibhav Gupta, Barry Bradlyn

摘要:

本文利用Wannier函数分析了一维光子晶体的拓扑相变。我们首先回顾了一维指数局域Wannier函数的构造,并展示了如何在光子系统中数值构造它们。然后,我们应用这些工具来研究光子模拟的苏-施里弗-希格模型。我们利用光子Wannier函数建立了一个精确定量的拓扑相变近似模型,并计算了拓扑缺陷态的局域化。最后,我们讨论了我们的工作对光子晶体能带表示研究的影响。

英文摘要:

In this work, we use Wannier functions to analyze topological phase transitions in one dimensional photonic crystals. We first review the construction of exponentially localized Wannier functions in one dimension, and show how to numerically construct them for photonic systems. We then apply these tools to study a photonic analog of the Su-Schrieffer-Heeger model. We use photonic Wannier functions to construct a quantitatively accurate approximate model for the topological phase transition, and compute the localization of topological defect states. Finally, we discuss the implications of our work for the study of band representations for photonic crystals.

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