通过波函数零点对能带拓扑进行实空间成像
Real-Space Imaging of Band Topology via Wavefunction Zeros
浏览论文内容
中文总结 AI 辅助
该研究利用新不变量证明晶体波函数在特定位置有对称强制零点，可借此推断电子能带拓扑，将扫描隧道显微镜与群表示理论联系，还应用于多种模型并揭示零点对相互作用效应的影响。
中文摘要 AI 辅助
我们证明，利用由波函数的对称对称表示唯一确定的新不变量，晶体在高对称动量\(\Psi_{\boldsymbol{k}_*}(\boldsymbol{r})\)处的波函数在晶胞的特定位置具有对称强制零点。这使得人们能够通过探测电荷密度的零点来推断电子能带的拓扑结构，进而将扫描隧道显微镜与能带结构的群表示理论联系起来。我们将该定理应用于1H过渡金属二卤化物，它检测到WSe₂的受阻原子极限；应用于Haldane模型，它检测到陈数模三；应用于Bernevig-Hughes-Zhang模型，它检测到\(\mathbb{Z}_2\)指标。此外，这些零点对相互作用效应有重要影响：在kagome金属中，它们确定了范霍夫波函数的亚晶格结构；在扭曲双层石墨烯中，它们解释了相互作用引起的平带定性重塑。
英文摘要
We prove that the wavefunction of a crystal at a high-symmetry momentum, $Ψ_{\boldsymbol{k}_*}(\boldsymbol{r})$, has symmetry-enforced zeros at certain positions in the unit cell, using a new invariant fixed uniquely by the symmorphic symmetry representation of the wavefunction. This allows one to infer the topology of an electronic band by probing zeros of the charge density, and in turn to connect scanning tunnelling microscopy to the group representation theory of bandstructure. We apply the theorem to 1H transition metal dichalcogenides, where it detects the obstructed atomic limit of WSe$_2$, the Haldane model, where it detects the Chern number modulo three, and the Bernevig-Hughes-Zhang model, where it detects the $\mathbb{Z}_2$ index. In addition, the zeros have important consequences for interaction effects: in kagome metals, they fix the sublattice structure of Van Hove wavefunctions, and in twisted bilayer graphene, they explain the qualitative interaction-induced reshaping of the flat bands.
