超越半经典方法的可观测量运动方程中的多带效应
Multiband Effects in Equations of Motion of Observables Beyond the Semiclassical Approach
摘要：
本文研究了Bloch电子多带波包的位置不变和规范不变晶体动量的运动方程。对于与晶体的其余能带结构分离良好的带的子集中的定域包，可以构造关于包的中心的有效电磁哈密顿量。我们表明，运动方程可以通过投影算子程序，这是来自微扰理论内的绝热近似。这些关系明确地包含从每个频带中捕获的展开系数和能量能带结构的布洛赫状态，以及非阿贝尔功能源于带间Berry相位特性的信息。这种通用和透明的基于哈密顿的方法被应用到一个波包分布在一个单一的频带，一组简并带，和两个线性交叉带。广义运动方程有望在传输电流和霍尔效应现象的新效果。
英文摘要：
The equations of motion for the position and gauge invariant crystal momentum are considered for multiband wave packets of Bloch electrons. For a localized packet in a subset of bands well-separated from the rest of the band structure of the crystal, one can construct an effective electromagnetic Hamiltonian with respect to the center of the packet. We show that the equations of motion can be obtained via a projection operator procedure, which is derived from the adiabatic approximation within perturbation theory. These relations explicitly contain information from each band captured in the expansion coefficients and energy band structure of the Bloch states as well as non-Abelian features originating from interband Berry phase properties. This general and transparent Hamiltonian-based approach is applied to a wave packet spread over a single band, a set of degenerate bands, and two linear crossing bands. The generalized equations of motion hold promise for novel effects in transport currents and Hall effect phenomena.
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