论文标题
无限双曲线晶格的高维表示的带理论和边界模式
Band theory and boundary modes of high-dimensional representations of infinite hyperbolic lattices
论文作者
论文摘要
双曲线空间中的周期晶格的特征是欧几里得晶体学组以外的对称性，为经典和量子波提供了一个新的平台，为新的拓扑超材料提供了巨大的潜力。双曲线晶格的一个重要特征是，与欧几里得晶格中的阿贝尔翻译组相比，它们的翻译组是非亚伯式的，允许高维不可减少表示形式（IRREPS）。在这里，我们介绍了一个通用框架，以构建无限双曲线晶格的高维无rrep的波征本态，从而概括了Bloch的定理，并讨论了其对双曲线晶格中不寻常的模式计算和退化的影响。我们将此方法应用于机械双曲线晶格，并将其带状结构和高维透明的零模式表征。
Periodic lattices in hyperbolic space are characterized by symmetries beyond Euclidean crystallographic groups, offering a new platform for classical and quantum waves, demonstrating great potentials for a new class of topological metamaterials. One important feature of hyperbolic lattices is that their translation group is nonabelian, permitting high-dimensional irreducible representations (irreps), in contrast to abelian translation groups in Euclidean lattices. Here we introduce a general framework to construct wave eigenstates of high-dimensional irreps of infinite hyperbolic lattices, thereby generalizing Bloch's theorem, and discuss its implications on unusual mode-counting and degeneracy, as well as bulk-edge correspondence in hyperbolic lattices. We apply this method to a mechanical hyperbolic lattice, and characterize its band structure and zero modes of high-dimensional irreps.
