论文标题
高阶拓扑双曲线晶格
Higher-order Topological Hyperbolic Lattices
论文作者
论文摘要
双曲线晶格允许任何$ p $折的旋转对称性与二维晶体形成鲜明对比，其中仅允许两倍，三倍，四倍或六倍旋转对称性。这种独特的功能激发了我们询问双曲线晶格中富集的旋转对称性是否可以导致晶体材料以外的任何新的拓扑阶段。在这里，通过在双曲线晶格中构建和探索紧密结合模型，我们从理论上证明了在双曲线晶格中存在高阶拓扑阶段，其中具有八倍，十二倍，十二倍，十六倍或二十倍或二十倍旋转的对称性，在结晶晶格中不允许使用。由于这种模型尊重时间反转对称性和$ p $ -fold（$ p = $ 8、12、16或20）旋转对称性的组合，因此保护了$ p $ Zero-Energy角模式。对于双曲线\ {8,3 \}晶格，我们发现一个间隙，一个无间隙和一个重入的高阶拓扑双曲线相位。重新进入阶段是由有限尺寸的效果产生的，该效果打开边缘状态的间隙，而角度模式的间隙不变。因此，我们的结果为研究双曲线晶格中的高阶拓扑阶段打开了大门。
A hyperbolic lattice allows for any $p$-fold rotational symmetry, in stark contrast to a two-dimensional crystalline material, where only twofold, threefold, fourfold or sixfold rotational symmetry is permitted. This unique feature motivates us to ask whether the enriched rotational symmetry in a hyperbolic lattice can lead to any new topological phases beyond a crystalline material. Here, by constructing and exploring tight-binding models in hyperbolic lattices, we theoretically demonstrate the existence of higher-order topological phases in hyperbolic lattices with eight-fold, twelve-fold, sixteen-fold or twenty-fold rotational symmetry, which is not allowed in a crystalline lattice. Since such models respect the combination of time-reversal symmetry and $p$-fold ($p=$8, 12, 16 or 20) rotational symmetry, $p$ zero-energy corner modes are protected. For the hyperbolic \{8,3\} lattice, we find a gapped, a gapless and a reentrant gapped higher-order topological hyperbolic phases. The reentrant phase arises from finite-size effects, which open the gap of edge states while leave the gap of corner modes unchanged. Our results thus open the door to studying higher-order topological phases in hyperbolic lattices.
