外电磁场下驱动非均匀绝缘体中旋量拓扑效应的半经典处理
A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
AI总结：
本文提出了一种半经典方法，处理外电磁场下绝热驱动、弱非均匀绝缘体中旋量自由度的输运与积累，推导了三阶自旋电流与密度，并将其与高维相空间的自旋Chern通量及多极矩理论相联系。
摘要：
在拓扑绝缘体的描述中引入内部自由度，带来了众多理论和实验进展。特别令人感兴趣的是时间或空间上的周期性扰动效应，因为它们极大地丰富了电子响应的多样性，例如Thouless电荷泵及其高维类似物，或高阶拓扑绝缘体。在此，我们开发了一种半经典方法，用于处理在绝热驱动、弱非均匀的一维、二维和三维绝缘体中，一般旋量自由度（如物理自旋、谷或原子轨道）的输运与积累，且系统处于外部电磁场下。具体而言，我们聚焦于物理自旋，推导了直至系统时空调制三阶的自旋电流和自旋密度。随后，我们将这些贡献与几何和拓扑对象——自旋Chern通量和自旋Chern数——联系起来，这些对象定义在系统的高维相空间中，即其组合的动量-位置-时间坐标。此外，通过引入电偶极矩、四极矩和八极矩的自旋类比，我们提供了半经典分析与现代多极矩理论之间的联系。这些结果在具体的紧束缚模型中得到了展示，其中诱导响应被解析地计算出来。
英文摘要：
Introducing internal degrees of freedom in the description of topological insulators has led to a myriad of theoretical and experimental advances. Of particular interest are the effects of periodic perturbations, either in time or space, as they considerably enrich the variety of electronic responses, with examples such as Thouless's charge pump and its higher dimensional cousins, or, higher-order topological insulators. Here, we develop a semiclassical approach to transport and accumulation of general spinor degrees of freedom, such as physical spin, valley, or atomic orbits, in adiabatically driven, weakly inhomogeneous insulators of dimensions one, two and three under external electromagnetic fields. Specifically, we focus on physical spins and derive the spin current and density up to third order in the spatio-temporal modulations of the system. We, then, relate these contributions to geometrical and topological objects -- the spin-Chern fluxes and numbers -- defined over the higher-dimensional phase-space of the system, i.e., its combined momentum-position-time coordinates. Furthermore, we provide a connection between our semiclassical analysis and the modern theory of multipole moments by introducing spin analogues of the electric dipole, quadrupole and octapole moments. The results are showcased in concrete tight-binding models where the induced responses are calculated analytically.
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