Giant Intrinsic Spin-Orbit Coupling in Bilayer Graphene

Details Giant Intrinsic Spin-Orbit Coupling in Bilayer Graphene Giant Intrinsic Spin-Orbit Coupling in Bilayer Graphene

2010-04-06

arxiv.org/abs/1004.0881v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 2 figures.

Scientific paper

The intrinsic spin-orbit coupling (ISOC) in bilayer graphene is investigated. We find that the largest ISOC between $\pi$ electrons origins from the following hopping processes: a $\pi$ electron hops to $\sigma$ orbits of the other layer and further to $\pi$ 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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