ABSTRACT
When dealing with quantum effects, or a combination of classical and quantum effects, two possibilities exist. The first is to use a model Hamiltonian such as the Huckel model, Hubbard model, tight-binding model. This approach is appealing if the model really reflects reality, but it heavily depends on one’s understanding and experience of a particular system. The second approach is to use an ab initio method to describe the system in a possibly exact manner, and to extract the studied effects from the system’s Hamiltonian. Solids contain lots of ions and electrons, and they come with different forms. Some are amorphous, some contain disorders and impurities, and some are crystallines. Spin-orbit coupling is an important interaction in ultrafast phenomena, and is directly responsible for intersystem crossing, spin-orbit torques in spintronics and demagnetization. Ultrafast phenomena introduce some special features to vector potentials. Because they are auxiliary fields, whether the results depend on our choice of these fields should be tested.
