AI 中文总结
研究各向异性蜂窝晶格中单个空位引发的拓扑相变，通过分析狄拉克谷变化及相关条件，揭示了拓扑相变机制，还介绍了缺陷零模变化及波前位错成像，为拓扑相变研究提供新视角。
AI 中文摘要
一个缺失的原子可以在一个对于其所有参数值原本平凡的晶格中驱动拓扑相变。我们在具有各向异性最近邻跳跃比率\(t'/t\)的二维蜂窝晶格中证明了这一点。根据尼尔森 - 尼诺米亚费米子加倍定理，原始晶格对于所有\(t'/t\)都是拓扑平凡的：狄拉克谷成对出现，其拓扑电荷在任何体不变量中完全抵消。单个空位打破这种抵消，对于\(t'/t<2\)，它作为具有缺陷缠绕数\(\nu_3=\mp 1\)的内边界。在\(t'/t = 2\)时，两个狄拉克谷合并并湮灭；有效赝自旋自由度的数量从\(m = 2\)降至\(m = 1\)，违反了非平凡缠绕数所需的\(d + D + 1 = 2m\)条件。缠绕数降至\(\nu_3 = 0\)：在固定对称类（BDI）内的拓扑相变，完全由体里夫希茨相变驱动，且仅通过空位可观测到。缺陷零模从代数型（\(\sim 1/r\)）转变为更强的空间限制，其逆参与率在临界处达到尖锐最小值。局部态密度中的波前位错提供了\(\nu_3\)的直接、空间分辨图像，可在石墨烯以及光子和冷原子类似物中获取。
英文摘要
A single missing atom can drive a topological phase transition in a lattice that is otherwise trivial for all values of its parameters. We demonstrate this in a two-dimensional honeycomb lattice with anisotropic nearest-neighbor hopping ratio $t'/t$. The pristine lattice is topologically trivial for all $t'/t$ by the Nielsen-Ninomiya fermion-doubling theorem: Dirac valleys appear in pairs whose topological charges cancel identically in any bulk invariant. A single vacancy breaks this cancelation, acting as an internal boundary with defect winding number $ν_3=\mp 1$ for $t'/t<2$. At $t'/t=2$, the two Dirac valleys merge and annihilate; the number of active pseudospinor degrees of freedom drops from $m=2$ to $m=1$, violating the condition $d+D+1=2m$ required for a non-trivial winding number. The winding number collapses to $ν_3=0$: a topological phase transition within a fixed symmetry class (BDI), driven entirely by a bulk Lifshitz transition and observable only through the vacancy. The defect zero mode crosses over from algebraic (${\sim}1/r$) to stronger spatial confinement, with its inverse participation ratio reaching a sharp minimum at criticality. Wavefront dislocations in the local density of states provide a direct, spatially resolved image of $ν_3$, accessible in graphene and in photonic and cold-atom analogs.
Comments14 pages, 7 figures
