Multipole theory of optical spatial dispersion in crystals
Multipole theory of optical spatial dispersion in crystals
复制标题
晶体中光学空间色散的多极理论
作者：
'Oscar Pozo;Ivo Souza
自然光学活动是源自原子尺度上电磁场的弱空间不均匀性的效应的典型例子。在分子中，电磁多极理论很好地描述了这种效应，其中与光的耦合在电偶极近似之外被半经典地处理。该理论有两个缺点：它仅限于有界系统，其构建模块——多极转变矩——与原点相关。在这项工作中，我们以平移不变的形式重塑了多极理论，这种形式对晶体仍然有效。在独立粒子近似中，我们引入了“本征”多极跃迁矩，它们与原点无关，并且在布洛赫本征态的规范变换下进行协变变换。电偶极子跃迁由带间贝里连接给出，而磁偶极子和电四极子跃迁由本征磁矩和量子度量的矩阵概括来描述。除了类多极项之外，光波矢中晶体的一阶响应还包含在分子理论中没有对应项的带色散项。完整的响应被分解为磁电和四极部分，它们可以在电场和磁场解耦的静态极限中被隔离。发现晶体的旋转强度和规则等效于平衡状态下消失的手性磁效应的拓扑约束，并且通过数值紧束缚计算验证了形式主义。
Natural optical activity is the paradigmatic example of an effect originating in the weak spatial inhomogeneity of the electromagnetic field on the atomic scale. In molecules, such effects are well described by the multipole theory of electromagnetism, where the coupling to light is treated semiclassically beyond the electric-dipole approximation. That theory has two shortcomings: it is limited to bounded systems, and its building blocks -the multipole transition moments- are origin dependent. In this work, we recast the multipole theory in a translationally-invariant form that remains valid for crystals. Working in the independent-particle approximation, we introduce "intrinsic" multipole transition moments that are origin independent and transform covariantly under gauge transformations of the Bloch eigenstates. Electric-dipole transitions are given by the interband Berry connection, while magnetic-dipole and electric-quadrupole transitions are described by matrix generalizations of the intrinsic magnetic moment and quantum metric. In addition to multipole-like terms, the response of crystals at first order in the wavevector of light contains band-dispersion terms that have no counterpart in molecular theories. The full response is broken down into magnetoelectric and quadrupolar parts, which can be isolated in the static limit where electric and magnetic fields become decoupled. The rotatory-strength sum rule for crystals is found to be equivalent to the topological constraint for a vanishing chiral magnetic effect in equilibrium, and the formalism is validated by numerical tight-binding calculations.
DOI：
10.1103/physrevb.103.045401
发表时间：
2020-02
期刊：
arXiv: Mesoscale and Nanoscale Physics
影响因子：
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作者：
C. Xiao;Huiying Liu;Jianzhou Zhao;Shengyuan A. Yang;Q. Niu
通讯作者：
C. Xiao;Huiying Liu;Jianzhou Zhao;Shengyuan A. Yang;Q. Niu