Bloch电子与外电磁场的相互作用及相互作用中的Bloch电子
Bloch electrons interacting with an external electromagnetic field and Bloch electrons in interaction
摘要：
我们适用于最近开发的一般方法推导的对角表示的任意矩阵值的量子哈密顿的特定情况下，布洛赫电子在外部电磁场。我们发现在$\hbar .$中对角表示是一个二阶级数展开。这个结果是确定不同能带间相互作用Bloch电子的有效带内哈密顿量的基础。实际上，描述诸如由完整电磁相互作用的磁性部分介导的磁矩-磁矩相互作用的效应需要在$\hbar $中进行二阶计算。结果表明，电子流由两部分组成：第一部分来自速度，第二部分是类似于狄拉克粒子自旋流的磁矩流.这最后的贡献是负责磁矩之间的相互作用类似的自旋自旋相互作用的Breit哈密顿狄拉克电子的相互作用。
英文摘要：
We apply a general method developed recently for the derivation of the diagonal representation of an arbitrary matrix valued quantum Hamiltonian to the particular case of Bloch electrons in an external electromagnetic field. We find the diagonal representation as a series expansion to the second order in $\hbar .$ This result is the basis for the determination of the effective in-band Hamiltonian of interacting Bloch electrons living in different energy bands. Indeed, the description of effects such as magnetic moment-moment interactions mediated by the magnetic part of the full electromagnetic interaction requires a computation to second order in $\hbar $. It is found that the electronic current is made of two contributions: the first one comes from the velocity and the second one is a magnetic moment current similar to the spin current for Dirac particles. This last contribution is responsible for the interaction between magnetic moments similarly to the spin-spin interaction in the Breit Hamiltonian for Dirac electrons in interaction.
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