发表机构
Shanghai University; Sorbonne Université（上海大学; 索邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对截-投影法生成的二元紧束缚链，探究其反演对称拓扑绝缘体的电子性质，明确了拓扑相变的判定条件及相关绝热路径的存在情况。
AI 中文摘要
我们研究了通过截-投影法生成的二元紧束缚链的电子性质，该链对应有理斜率α=p/q，形成具有n=p+q个位点的周期且反演对称的链。二元结构由两个跳跃振幅tₐ和t_b编码。在固定tₐ≠t_b的情况下，能谱随p/n变化的支撑区域形成了“截-投影蝴蝶”。我们聚焦于总n个能带中填充了M个能带的绝缘体，并改变tₐ/t_b。反演对称性约束电极化P为0或P_q/2（模极化量子P_q = gcd(M,n)/n）。当且仅当n/gcd(M,n)为奇数时，两个具有量化极化的绝缘体之间会发生拓扑相变；当n/gcd(M,n)为偶数时，尽管在tₐ=t_b时能隙闭合，但两个绝缘区域的极化均为零，不会发生拓扑相变。当n为偶数且M为奇数时，我们发现一条介于tₐ>t_b和tₐ<t_b之间的绝热路径，该路径可维持反演对称性和能隙。
英文摘要
We investigate the electronic properties of binary tight-binding chains generated by the cut-and-project method for rational slopes $α=p/q$, leading to periodic and inversion symmetric chains with $n=p+q$ sites. The binary structure is encoded in two hopping amplitudes $t_a$ and $t_b$. For fixed $t_a \neq t_b$, the support of the energy spectrum as a function of $p/n$ gives rise to a "Cut-and-Project butterfly". We concentrate on insulators with $M$ filled bands among a total of $n$ bands and vary $t_a/t_b$. Inversion symmetry constrains the electric polarization $P$ to $0$ or $P_q/2$ modulo a polarization quantum $P_q = \gcd(M,n)/n$. A topological transition, between two insulators that differ by their quantized polarization, occurs if and only if $n/\gcd(M,n)$ is odd. When $n/\gcd(M,n)$ is even, the two insulating regimes have a vanishing polarization and no topological transition occurs, despite the gap closing at $t_a=t_b$. When $n$ is even and $M$ odd, we find an adiabatic path between $t_a>t_b$ and $t_a<t_b$ that maintains inversion symmetry and a gap.
