光谱重量：弱和强自旋轨道耦合的比较
Optical spectral weight: comparison of weak and strong spin-orbit coupling
摘要：
自旋电子半导体的费米速度（$v_{F}$）与自旋轨道耦合有关，比拓扑绝缘体的费米速度小两个数量级。这两个族都可以用相同的哈密顿量来处理，其中包含一个与$v_{F}$成比例的相对论性（狄拉克）动量项和一个与薛定谔质量（m）成比例的非相对论性二次贡献。我们发现，交流动态纵向和横向（霍尔）磁导率是强烈依赖于$v_{F}$的大小。与拓扑绝缘体相比，当狄拉克费米速度较小时，由带间光学跃迁提供的吸收背景仅在非常有限的光子能量范围内是有限的。它的起始取决于化学势（$μ$）和磁场（B）的值，它的上限也是如此。然而，在该有限范围内，其量值是恒定的，并且具有与在拓扑绝缘体中以及石墨烯中发现的相同的$e^{2}π/(8h)$量值，注意到简并因子的差异。通用带间背景下的总光谱权重为$e^{2}π/(8h)4mv_{F}^{2}$。与石墨烯的已知结果相反，当非相对论贡献存在于哈密顿量中时，无论其大小如何，没有严格的守恒定律适用于由化学势的大小变化引起的带间和带内跃迁之间的光谱权重转移。
英文摘要：
The Fermi velocity ($v_{F}$) associated with the spin-orbit coupling is two orders of magnitude smaller for spintronic semiconductors than it is for topological insulators. Both families can be treated with the same Hamiltonian which contains a relativistic (Dirac) linear in momentum term proportional to $v_{F}$ and a non-relativistic quadratic contribution with Schrödinger mass (m). We find that the AC dynamic longitudinal and transverse (Hall) magneto-conductivities are strongly dependent on the size of $v_{F}$. When the Dirac fermi velocity is small, the absorption background provided by the interband optical transitions is finite only over a very limited range of photon energies as compared with topological insulators. Its onset depends on the value of the chemical potential ($μ$) and on the magnetic field (B), as does its upper cut off. Within this limited range its magnitude is however constant and has the same magnitude of $e^{2}π/(8h)$ as is found in topological insulators and also in graphene noting a difference in degeneracy factor. The total optical spectral weight under the universal interband background is $e^{2}π/(8h)4mv_{F}^{2}$. In contrast to the known result for graphene no strict conservation law applies to the spectral weight transfers between inter and intra band transition brought about by variations in the magnitude of the chemical potential when a non-relativistic contribution is present in the Hamiltonian whatever size it may have.
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