Insulating systems are characterized by their insensitivity to twisted boundary conditions as quantified by the charge stiffness and charge localization length. The latter quantity was shown to be related to the expectation value of the many-body position operator and serves as a universal criterion to distinguish between metals and insulators. In this work we extend these concepts to a new class of quantum systems having conserved charge and dipole moments. We refine the concept of a charge insulator by introducing notions of multipolar insulators, e.g., a charge insulator could be a dipole insulator or dipole metal. We develop a universal criterion to distinguish between these phases by extending the concept of charge stiffness and localization to analogous versions for multipole moments, but with our focus on dipoles. We are able relate the dipole localization scale to the expectation value of a recently introduced many-body quadrupole operator. This refined structure allows for the identification of phase transitions where charge remains localized but, e.g., dipoles delocalize. We illustrate the proposed criterion using several exactly solvable models that exemplify these concepts, and discuss a possible realization in cold-atom systems.
"Nonmagnetic" Dimer Mott insulator induced by the coupling of spin with quantum electric dipoles
基于强耦合分析，提出了一个有效的偶极自旋模型，该模型可以解释“自旋液体莫特绝缘体“的可能起源。这个问题与二聚体莫特绝缘体有关，它使人联想到有机三角晶格系统$κ$ Cu $_2$（CN）$_3$，它的无隙自旋液态已经在二聚体轨道上自旋之间交换耦合的几何阻挫（$J$）的背景下讨论过。事实证明，绝缘体中的另一个自由度，二聚体上的{ \it量子电偶极子}，通过库仑相互作用彼此相互作用，并通过偶极-自旋耦合带来对$J$的显著抑制。
Intrinsic surface dipole in topological insulators
利用密度泛函理论计算了两种典型拓扑绝缘体（Bi $_2$ Se $_3$和Bi $_2$ Te $_2$ Se）的局域态密度随离表面距离的变化.我们发现，在没有无序或掺杂的情况下，存在一个2 nm厚的表面偶极子，其起源是占据狄拉克点以上的拓扑表面态。因此，导带的底部在表面附近向上弯曲约75 meV，并且存在与价带的顶部相关联的驼峰状特征。我们预期，只要费米能级不越过狄拉克点，能带弯曲将发生在所有原始的拓扑绝缘体中。结果表明，拓扑绝缘体是本征肖特基势垒太阳能电池。
Anomalous dielectric response in the dimer Mott insulator $κ$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$
我们测量和分析了二聚体莫特绝缘体$κ-$（BEDT-TTF）$_2$ Cu $_2$（CN）$_3$的介电常数，它被称为自旋液体状态的操场。最出乎意料的是，这种特定的有机盐具有非平凡的电荷自由度，其特征在于低于约60 K的偶极玻璃样介电弛豫。这归因于二聚体内的电荷分离，由于位间库仑排斥。在这方面，这里观察到的偶极子是纯粹的量子力学，从而表现出意想不到的响应。
霍普夫绝缘体是一种弱拓扑绝缘体，其特征是绝缘体的导电边缘态被整数值连接数不变量保护。该态存在于三维双带模型中。我们证明了霍普夫绝缘体可以自然地实现在晶格的偶极相互作用的自旋，自旋交换中起着粒子跳跃的作用。偶极-偶极相互作用的长程各向异性性质允许动量-空间结构中所需的精确细节，而不同的自旋取向确保了跳跃的复杂相的必要结构。我们的模型具有强大的无隙边缘状态在两个光滑的边缘，以及锐边服从一定的晶体对称性，尽管在后者的两个波段的图片故障。在配套手稿[2105.10504]中，我们提供了使用超冷极性分子$^{40}$ K $^{87}$ Rb实施我们建议的具体实验蓝图。
