拓扑碳化钌（RuC）和碳化锇（OsC）单层的对称约束低能有效哈密顿量
Symmetry-constrained low-energy effective Hamiltonian for topological RuC and OsC monolayers
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中文总结 AI 辅助
研究碳化钌和碳化锇单层，通过对称性分析构建多带\(\mathbf{k}\cdot\mathbf{p}\)哈密顿量并简化为四带低能模型，其有效哈密顿量具特殊形式，拟合参数可重现低能区能带结构，为分析其电子和拓扑性质提供紧凑模型。
中文摘要 AI 辅助
我们推导了平面六角构型的碳化锇（OsC）和碳化钌（RuC）单层的低能\(\mathbf{k}\cdot\mathbf{p}\)有效哈密顿量。第一性原理计算表明这两种单层都是动态稳定的，并表现出二维量子自旋霍尔（QSH）相的特征，具有非平凡的\(\mathbb{Z}_2\)拓扑不变量。利用\(\Gamma\)点的对称性分析，我们构建了一个包含自旋轨道耦合的多带\(\mathbf{k}\cdot\mathbf{p}\)哈密顿量，并通过洛丁分区将其简化为一个四带低能模型。该有效哈密顿量具有块对角形式，两个块通过时间反演对称相关，类似于贝内维格 - 休斯 - 张（BHZ）模型。与标准BHZ形式不同，对称允许的非对角耦合包含二次动量相关项，这改变了\(\Gamma\)点附近的低能色散。拟合参数在低能区域重现了从头算能带结构，为分析单层OsC和RuC的电子和拓扑性质提供了一个紧凑模型。
英文摘要
We derive a low-energy $\mathbf{k}\cdot\mathbf{p}$ effective Hamiltonian for monolayer osmium carbide (OsC) and ruthenium carbide (RuC) in a planar hexagonal configuration. First-principles calculations indicate that both monolayers are dynamically stable and exhibit features of a two-dimensional quantum spin Hall (QSH) phase, characterized by a nontrivial $\mathbb{Z}_2$ topological invariant. Using symmetry analysis at the $Γ$ point, we construct a multiband $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian including spin-orbit coupling and reduce it to a four-band low-energy model through Löwdin partitioning. The effective Hamiltonian has a block-diagonal form, with two blocks related by time-reversal symmetry, analogous to the Bernevig--Hughes--Zhang (BHZ) model. In contrast to the standard BHZ form, the symmetry-allowed off-diagonal coupling contains quadratic momentum-dependent terms, which modify the low-energy dispersion near the $Γ$ point. The fitted parameters reproduce the ab initio band structures in the low-energy region, yielding a compact model for analyzing the electronic and topological properties of monolayer OsC and RuC.
