论文标题
准晶体中分数拓扑角模式的有效模型
Effective Model for Fractional Topological Corner Modes in Quasicrystals
论文作者
论文摘要
High-order topological insulators (HOTIs), as generalized from topological crystalline insulators (TCIs), are characterized with lower-dimensional metallic boundary states protected by spatial symmetries of a crystal, whose theoretical framework based on band inversion at special $k$-points cannot be readily extended to quasicrystals because quasicrystals contain rotational symmetries that are not compatible with crystals, and动量不再是一个良好的量子数。在这里，我们为所有可能的旋转对称性的2D准晶体中的HOTI状态下开发了一个低能的有效模型。通过实施最近针对准晶体开发的新型傅立叶变换，并通过其大规模平均值近似长波长的行为，我们构建了一个有效的$ k \ cdot p $ hamiltonian，以捕获伪brillouin Zone（PBZ）中心的频段倒置。我们表明，平面内的Zeeman场可以在2D准晶体Ti的相邻边缘的交点上诱导大规模弯曲，并通过旋转对称性保护具有分数电荷的角模式（CMS）（CMS）。我们的模型预测通过数值紧密结合计算证实。此外，当准晶体被\ textit {s} - 波超导体邻近时，也可以通过调整田间强度和化学潜力来创建majoraana cms。我们的工作提供了一种与拓扑激发和分数统计有关的准晶体低能物理学的通用方法。
High-order topological insulators (HOTIs), as generalized from topological crystalline insulators (TCIs), are characterized with lower-dimensional metallic boundary states protected by spatial symmetries of a crystal, whose theoretical framework based on band inversion at special $k$-points cannot be readily extended to quasicrystals because quasicrystals contain rotational symmetries that are not compatible with crystals, and momentum is no longer a good quantum number. Here, we develop a low-energy effective model underlying HOTI states in 2D quasicrystals for all possible rotational symmetries. By implementing a novel Fourier transform developed recently for quasicrystals and approximating the long-wavelength behavior by their large-scale average, we construct an effective $k \cdot p$ Hamiltonian to capture the band inversion at the center of a pseudo-Brillouin zone (PBZ). We show that an in-plane Zeeman field can induce mass-kinks at the intersection of adjacent edges of a 2D quasicrystal TI and generate corner modes (CMs) with fractional charge, protected by rotational symmetries. Our model predictions are confirmed by numerical tight-binding calculations. Furthermore, when the quasicrystal is proximitized by an \textit{s}-wave superconductor, Majorana CMs can also be created by tuning the field strength and chemical potential. Our work affords a generic approach to studying the low-energy physics of quasicrystals, in association with topological excitations and fractional statistics.
