位移电流的精确涡旋分解

中文摘要 AI 辅助

在位移电流中，是否有任何整数得以存留，并且陈数是否控制其符号？我们证明位移矢量是布里渊环面上的奇异场。其旋度有两个来源：带间贝里曲率和跃迁偶极子零点处的量子化点电荷。反转这一关系，可以得到位移电导率的精确分解，该分解在每个频率下均有效，分解为一个与整数电荷线性相关的部分和三个连续部分。作为测试平台，我们采用石墨烯-霍尔丹双层结构：该模型使我们能够在固定能隙下将带间陈数扫过五个值，以隔离其作用。我们还针对时间反演对称的偏置AB双层结构测试了该形式体系。每当一个电荷位于带边，并且存在三角翘曲时，仅整数部分就能解释带边峰。相关的整数不是陈数，而是该单个电荷的绕数。其符号与谷依赖的轮廓相结合，决定了光电流的符号。在这些双层结构中，跨越拓扑转变的符号反转遵循该绕数；只有当同一个能隙闭合同时影响两者时，不变量才随之改变。带边电荷不需要不变量。它仅要求两个带边子格不被最近邻跳跃连接，而三角翘曲使其可见。

英文摘要

Does any integer survive in the shift current, and does the Chern number control its sign? We show that the shift vector is a singular field on the Brillouin torus. Its curl has two sources: the interband Berry curvature and quantised point charges at the zeros of the transition dipole. Inverting this relation gives an exact decomposition of the shift conductivity, valid at every frequency, into one sector linear in the integer charges and three continuous sectors. As a testing ground, we take a graphene-Haldane bilayer: a model that lets us sweep the interband Chern number through five values at fixed gap to isolate its role. We also test the formalism against the time-reversal-symmetric biased AB bilayer. Whenever a charge sits at the band edge, and trigonal warping is present, the integer sector alone accounts for the band-edge peak. The relevant integer is not the Chern number but the winding of that single charge. Its sign, combined with a valley-dependent profile, sets the sign of the photocurrent. In these bilayers, sign reversals across topological transitions follow this winding; the invariant changes with it only when the same gap closing does both. A band-edge charge needs no invariant. It only requires that the two band-edge sublattices not be connected by the nearest-neighbour hopping, and trigonal warping makes it visible.

发表机构

• Universidad Técnica Federico Santa María（弗雷德里科·Santa玛丽亚技术大学）
• Universidad Central de Chile（智利中央大学）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

3 pages, 6 figures, 2 appendices