电子的六重激发
Six-fold Excitations in Electrides
摘要：
在凝聚态物理中，由于缺乏完全的旋转对称性，固体表现出狄拉克和外尔费米子之外的新激发，其中六重激发由于玻色子系统中最大简并的存在而引起了人们的极大兴趣。在这里，我们提出了一个单一的线性色散六重激发可以发现在锂$_{12}$镁$_3$硅$_4$及其衍生物。六重激发由基本能带表示的浮带- $A@12a$ -形成，浮带源自以空位（${\it i.e.}$，$12a$ Wyckoff位置）为中心的过量电子。存在一个独特的拓扑体表面边缘对应的无自旋的六重激发，导致平凡的表面费米弧，但非平凡的铰链弧。所有能量带隙的$k_z$ -切片属于二维（2D）高阶拓扑绝缘相，其由组合对称性${\mathcal T}{\widetilde S_{4z}}$保护并且由量化分数角电荷$Q_{corner}=\frac{3|e|}{4}$表征。因此，铰链弧中得到的铰链频谱的$\widetilde S_{4z}$对称杆结构。具有单一六重激发的状态，由非对称晶体对称性和时间反转对称性稳定，位于相边界处，并且可以通过明确的对称性破缺而被驱动到各种拓扑不同的相中，使得这些晶体结构成为系统研究不同拓扑相的有希望的平台。
英文摘要：
Due to the lack of full rotational symmetry in condensed matter physics, solids exhibit new excitations beyond Dirac and Weyl fermions, of which the six-fold excitations have attracted considerable interest owing to the presence of the maximum degeneracy in bosonic systems. Here, we propose that a single linear dispersive six-fold excitation can be found in the electride Li$_{12}$Mg$_3$Si$_4$ and its derivatives. The six-fold excitation is formed by the floating bands of elementary band representation -- $A@12a$ -- originating from the excess electrons centered at the vacancies (${\it i.e.}$, the $12a$ Wyckoff sites). There exists a unique topological bulk-surface-edge correspondence for the spinless six-fold excitation, resulting in trivial surface 'Fermi arcs' but nontrivial hinge arcs. All energetically-gapped $k_z$-slices belong to a two-dimensional (2D) higher-order topological insulating phase, which is protected by a combined symmetry ${\mathcal T}{\widetilde S_{4z}}$ and characterized by a quantized fractional corner charge $Q_{corner}=\frac{3|e|}{4}$. Consequently, the hinge arcs are obtained in the hinge spectra of the $\widetilde S_{4z}$-symmetric rod structure. The state with a single six-fold excitation, stabilized by both nonsymmorphic crystalline symmetries and time-reversal symmetry, is located at the phase boundary and can be driven into various topologically distinct phases by explicit breaking of symmetries, making these electrides promising platforms for the systematic studies of different topological phases.
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