The intrinsic spin-orbit coupling (ISOC) in bilayer graphene is investigated. We find that the largest ISOC between π electrons origins from the following hopping processes: a π electron hops to σ orbits of the other layer and further to π orbits with the opposite spin through the intra-atomic ISOC. The magnitude of this ISOC is about 0.46meV, 100 times larger than that of the monolayer graphene. The Hamiltonians including this ISOC in both momentum and real spaces are derived. Due to this ISOC, the low-energy states around the Dirac point exhibit a special spin polarization, in which the electron spins are oppositely polarized in the upper and lower layers. This spin polarization state is robust, protected by the time-reversal symmetry. In addition, we provide a hybrid system to select a certain spin polarization state by an electric manipulation.
@article{arxiv.1004.0881,
title = {Giant Intrinsic Spin-Orbit Coupling in Bilayer Graphene},
author = {Hai-Wen Liu and X. C. Xie and Qing-feng Sun},
journal= {arXiv preprint arXiv:1004.0881},
year = {2015}
}