论文标题
平面系统中量子距离的散装界面对应关系
Bulk-interface correspondence from quantum distance in flat band systems
论文作者
论文摘要
宽大的对应关系是拓扑分析的不可或缺的特征，边界或界面模式的存在直接洞悉Bloch波函数的拓扑结构。虽然仅将波函数的拓扑与边界模式相关，但我们证明了另一种几何量，即所谓的量子距离，也可以托管一个宽敞的接口对应关系。我们考虑了一类二维平面系统的一类，在该系统中，平面带与另一个分散谱带具有抛物线带。虽然已知这种平坦的条带在拓扑上是微不足道的，但我们表明，在接触点围绕平坦条带之间的非零最大量子距离可确保在两个具有不同化学势或不同最大量子距离的域之间的接口上存在边界模式。此外，最大量子距离甚至可以预测界面模式的分散关系的明确形式。
The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the wave function has been considered relevant to boundary modes, we demonstrate that another geometric quantity, the so-called quantum distance, can also host a bulk-interface correspondence. We consider a generic class of two-dimensional flat band systems, where the flat band has a parabolic band-crossing with another dispersive band. While such flat bands are known to be topologically trivial, we show that the nonzero maximum quantum distance between the eigenstates of the flat band around the touching point guarantees the existence of boundary modes at the interfaces between two domains with different chemical potentials or different maximum quantum distance. Moreover, the maximum quantum distance can predict even the explicit form of the dispersion relation and decay length of the interface modes.
