论文标题
简化平坦波段的非平凡量子几何形状
Nontrivial quantum geometry of degenerate flat bands
论文作者
论文摘要
最近在许多情况下，量子指标在平板系统中的重要性已经注意到，例如超流体刚度，直流电导率和理想的Chern绝缘子。退化的量子度量和非成绩带的量子度量都可以通过不同的格拉曼尼亚歧管的几何形状自然描述，该谱系具有特异性的脱整流性。与（Abelian）浆果曲率相反，由于频段集合崩溃而导致的简化条带的量子度量不仅仅是单个量子指标的总和。我们从两个频段之间的过渡偶极矩阵元素方面提供了这种现象的物理解释。通过考虑玩具模型，我们表明量子指标会增强，减少或不受影响，具体取决于哪些频带崩溃。已知DC纵向电导率和超流体刚度与扁平频段系统的量子度量成正比，这使它们成为观察这种现象的合适候选者。
The importance of the quantum metric in flat-band systems has been noticed recently in many contexts such as the superfluid stiffness, the dc electrical conductivity, and ideal Chern insulators. Both the quantum metric of degenerate and nondegenerate bands can be naturally described via the geometry of different Grassmannian manifolds, specific to the band degeneracies. Contrary to the (Abelian) Berry curvature, the quantum metric of a degenerate band resulting from the collapse of a collection of bands is not simply the sum of the individual quantum metrics. We provide a physical interpretation of this phenomenon in terms of transition dipole matrix elements between two bands. By considering a toy model, we show that the quantum metric gets enhanced, reduced, or remains unaffected depending on which bands collapse. The dc longitudinal conductivity and the superfluid stiffness are known to be proportional to the quantum metric for flat-band systems, which makes them suitable candidates for the observation of this phenomenon.
