1 Spin-orbit interaction in Spin-orbit interaction in graphene graphene , , nanotubes nanotubes , fullerenes , fullerenes Graphene week-MPI PKS Dresden September 25-29 Spin-orbit interaction in graphene, nanotubes and fullerenes Daniel Daniel Huertas Huertas -Hernando -Hernando (NTNU) (NTNU) Francisco Guinea (ICMM-CSIC) Francisco Guinea (ICMM-CSIC) Arne Arne Brataas Brataas (NTNU) (NTNU) Phys. Rev. B Phys. Rev. B 74 74 , , …(2006) in print; (2006) in print; cond cond -mat/0606580. -mat/0606580.
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Spin-orbit interaction in Spin-orbit interaction in graphenegraphene, , nanotubesnanotubes, fullerenes, fullerenes
Graphene week-MPI PKS Dresden September 25-29
Spin-orbit interaction in graphene, nanotubes and fullerenes
Daniel Daniel HuertasHuertas-Hernando-Hernando (NTNU) (NTNU)Francisco Guinea (ICMM-CSIC)Francisco Guinea (ICMM-CSIC)Arne Arne Brataas Brataas (NTNU)(NTNU)
Phys. Rev. B Phys. Rev. B 7474, , ……(2006) in print;(2006) in print; cond cond-mat/0606580.-mat/0606580.
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H = Ψ† −i γ ⋅∇( ) Ψ
γ = vF σ x ,τ zσ y( ); vF =3γ oa2 5.3 eV
σ − A,B sublattice a 2.46 τ − K,K ' γ o 3eV
Spin-orbit interaction in graphene, nanotubes and fullerenes
Fig.Y.Zhang et. al.,Nature 438,201-204, (2005)
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Spin-orbit interaction in graphene, nanotubes and fullerenes
Is S-O important in graphene?:•Atomic Spin-Orbit is supposed to be rather weak in Carbon as Z=6:
•Is S-O in graphene small?: YES. How small and why!!!
•Spin Quantum Hall effect proposal by Kane&Mele.
•Controlling pseudo-spin by means of coupling to the spin!
•Spintronics in graphene:•Spin-flip due to S-O. How important ?