Topological dipole conserving insulators and multipolar responses
Topological dipole conserving insulators and multipolar responses
复制标题
拓扑偶极守恒绝缘体和多极响应
DOI：
10.1103/physrevb.104.085136
复制
发表时间：
2021
影响因子：
3.7
通讯作者：
T. Hughes
中科院分区：
文献类型：
--
作者：
Julian May;T. Hughes
高阶拓扑绝缘体（HOTI）是一种新型的绝缘量子物质，其特征是具有由无隙角态或铰链态分开的带隙边界。最近，有人提出，一个大类的HOTI的基本特征是由拓扑多极响应理论捕获。在这项工作中，我们表明，这些多极响应可以实现相互作用的晶格模型，既保存电荷和偶极子。在这项工作中，我们研究了几个模型中的强相互作用和平均场限制。在$2$D中，我们考虑了一个环交换模型，它具有四极响应，并且可以被调谐到具有半整数四极矩和半整数角电荷的$C_4$对称高阶拓扑相。然后，我们扩展了这个模型，开发一个相互作用的晶格模型中的绝热偶极泵浦的解析描述。四极矩的变化，在这个泵的过程中，如果这个过程是周期性的，我们表明在四极矩的总变化是量化为一个整数。我们还考虑了两个相互作用的3$D晶格模型与手征铰链模式。我们表明，手征铰链模式是最近提出的“偶极陈-西蒙斯”响应，这是有关的四极响应降维的预兆。有趣的是，我们发现，在平均场的限制，这两个$2$D和$3$D相互作用的模型，我们认为在这里是等价的非相互作用的HOTI（或边界阻塞版本）的已知模型。自洽平均场理论的治疗提供了洞察自由费米子（平均场）理论之间的连接具有消失的极化和相互作用的模型，其中偶极矩微观守恒。
Higher order topological insulators (HOTIs) are a novel form of insulating quantum matter, which are characterized by having gapped boundaries that are separated by gapless corner or hinge states. Recently, it has been proposed that the essential features of a large class of HOTIs are captured by topological multipolar response theories. In this work, we show that these multipolar responses can be realized in interacting lattice models, which conserve both charge and dipole. In this work we study several models in both the strongly interacting and mean-field limits. In $2$D we consider a ring-exchange model which exhibits a quadrupole response, and can be tuned to a $C_4$ symmetric higher order topological phase with half-integer quadrupole moment, as well as half-integer corner charges. We then extend this model to develop an analytic description of adiabatic dipole pumping in an interacting lattice model. The quadrupole moment changes during this pumping process, and if the process is periodic, we show the total change in the quadrupole moment is quantized as an integer. We also consider two interacting $3$D lattice models with chiral hinge modes. We show that the chiral hinge modes are heralds of a recently proposed"dipolar Chern-Simons"response, which is related to the quadrupole response by dimensional reduction. Interestingly, we find that in the mean field limit, both the $2$D and $3$D interacting models we consider here are equivalent to known models of non-interacting HOTIs (or boundary obstructed versions). The self-consistent mean-field theory treatment provides insight into the connection between free-fermion (mean-field) theories having vanishing polarization and interacting models where dipole moments are microscopically conserved.
影响因子：
64.8
作者：
Peterson, Christopher W.;Benalcazar, Wladimir A.;Bahl, Gaurav
通讯作者：
Bahl, Gaurav