论文标题
通用Benalcazar-Bernevig-Hughes模型的Wannier拓扑结构和四倍的时刻
Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
论文作者
论文摘要
我们使用量化的四极力矩分析了一种特殊的可分离和手性对称模型，扩展了Benalcazar-Bernevig-Hughes模型[Science 357，61（2017）]。使用Nested-Wilson循环形式主义，我们为Wannier中心，扇形极化和四极矩矩提供了精确的表达。这些连接到构成一维链的绕组数。我们证明，这些绕组数字可以将模型的Wannier拓扑描述为$ \ Mathbb {z} \ times \ times \ mathbb {z} $ set。这些结果清楚地表明，四极力矩的量化可能会出现，而没有其他空间对称性（除了翻译对称性除外）。通过从Wannier表示转换为Bloch表示形式，我们得出了散装四极力矩的替代表达式，并获得其确切值。结合了散装四极杆和边缘极化，我们通过分析计算大方形系统中的角电荷，并在边缘符合仪表仪中显式。我们的工作揭示了边界，电荷定位和扩展模型的大量四极杆的零能量状态之间的关系。
We analyze a special separable and chiral-symmetric model with a quantized quadrupole moment, extending the Benalcazar-Bernevig-Hughes model [Science 357, 61 (2017)]. Using nested-Wilson loop formalism, we give an exact expression for Wannier centers, sector polarizations, and quadrupole moments. These are connected to the winding numbers of the constitutive one-dimensional chains. We prove that these winding numbers can characterize the model's Wannier topology as a $\mathbb{Z}\times\mathbb{Z}$ set. These results clearly show that the quantization of the quadrupole moment can arise without additional spatial symmetry (except for translation symmetry) for the bulk. By switching from the Wannier representation to the Bloch representation, we derive an alternative expression for the bulk quadrupole moment and obtain its exact value. Combining the bulk quadrupole and edge polarizations, we analytically calculate the corner charge in a large square system and make the bulk-boundary correspondence explicit in an edge-consistent gauge. Our work reveals the relationship between zero-energy states at the boundary, charge localization, and the bulk quadrupole of the extended model.
