论文标题
周期系统中的角电荷和散装多极矩
Corner charge and bulk multipole moment in periodic systems
论文作者
论文摘要
二维周期系统得出了根据散装四极力矩的角度电荷的公式。这是根据块状极化的表面电荷密度的公式的类似物。在有$ n $ fold的旋转对称性的情况下，$ n = 3 $，$ 4 $和$ 6 $，四极力矩进行了量化，并且独立于Wannier Orbitals的传播或形状，仅取决于填充带的Wannier中心的位置。在这种情况下，我们的公式纯粹从散装特性预测四极力矩的分数部分。只要基态被覆盖并且在拓扑上琐碎的意义上，系统就可以包含多体相互作用。还讨论了这些结果向三维系统的扩展。通常，在三个维度上，即使在存在点组对称性的情况下，也从大量的角度看不完全预测角电荷的分数。
A formula for the corner charge in terms of the bulk quadrupole moment is derived for two-dimensional periodic systems. This is an analog of the formula for the surface charge density in terms of the bulk polarization. In the presence of an $n$-fold rotation symmetry with $n=3$, $4$, and $6$, the quadrupole moment is quantized and is independent of the spread or shape of Wannier orbitals, depending only on the location of Wannier centers of filled bands. In this case, our formula predicts the fractional part of the quadrupole moment purely from the bulk property. The system can contain many-body interactions as long as the ground state is gapped and topologically trivial in the sense it is smoothly connected to a product state limit. An extension of these results to three-dimensional systems is also discussed. In three dimensions, in general, even the fractional part of the corner charge is not fully predictable from the bulk perspective even in the presence of point group symmetry.
