Giant Intrinsic Spin-Orbit Coupling in Bilayer Graphene

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.

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