论文标题
三维二维晶体的理论
Theory of triangulene two-dimensional crystals
论文作者
论文摘要
等边三角形的石墨烯纳米群岛的横向尺寸为$ n $苯环，被称为$ [n] $ triangulenes。单个$ [n] $三角形是开放式壳分子，具有单粒子电子光谱，可容纳$ n-1 $ $ $半填充的零模式，并且具有旋转$ s =（n-1）/2 $的多体基础状态。三角形的表面合成以$ n = 3,4,5,7 $的形式证明，并且已经据报道，据报道，观察了haldane对称性保护的拓扑阶段$ [3] $ triangulenes。在这里，我们提供了一个统一的理论，用于二维蜂窝晶格家族的电子特性，其单位单元包含一对具有尺寸的三角形，$ n_a，n_b $。结合密度功能理论和紧密结合计算，我们发现了大量半填充的狭窄带，包括石墨烯般的频谱（$ n_a = n_b = 2 $），spin-1 dirac电子（$ n_a = 2，n_b = 3 $）传导带（$ n_a = n_b = 4 $）。所有这些结果都是通过在零能量状态的子空间上进行的一类有效的哈密顿人合理化的，这些有效的哈密顿量概括了石墨烯蜂窝模型，并以$ C_3 $对称性的内部假性自由度为fermions。
Equilateral triangle-shaped graphene nanoislands with a lateral dimension of $n$ benzene rings are known as $[n]$triangulenes. Individual $[n]$triangulenes are open-shell molecules, with single-particle electronic spectra that host $n-1$ half-filled zero modes and a many-body ground state with spin $S=(n-1)/2$. The on-surface synthesis of triangulenes has been demonstrated for $n=3,4,5,7$ and the observation of a Haldane symmetry-protected topological phase has been reported in chains of $[3]$triangulenes. Here, we provide a unified theory for the electronic properties of a family of two-dimensional honeycomb lattices whose unit cell contains a pair of triangulenes with dimensions $n_a,n_b$. Combining density functional theory and tight-binding calculations, we find a wealth of half-filled narrow bands, including a graphene-like spectrum (for $n_a=n_b=2$), spin-1 Dirac electrons (for $n_a=2,n_b=3$), $p_{x,y}$-orbital physics (for $n_a=n_b=3$), as well as a gapped system with flat valence and conduction bands (for $n_a=n_b=4$). All these results are rationalized with a class of effective Hamiltonians acting on the subspace of the zero-energy states that generalize the graphene honeycomb model to the case of fermions with an internal pseudospin degree of freedom with $C_3$ symmetry.
