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Comment: 15 pages. Submitted to the Proceedings of the ULTI symposium on Quantum Phenomena and Devices at Low Temperatures, Espoo, Finland, to be published in the Journ. of Low. Temp. Phys
The intrinsic spin-orbit interactions in bilayer graphene and in graphite are studied, using a tight binding model, and an intraatomic LS coupling. The spin-orbit interactions in bilayer graphene and graphite are larger, by about one order of magnitude, than the interactions in single layer graphene, due to the mixing of pi and sigma bands by interlayer hopping. Their value is in the range 0.1 - 1K. The spin-orbit coupling opens a gap in bilayer graphene, and it also gives rise to two edge modes. The spin-orbit couplings are largest, 1-4K, in orthorhombic graphite, which does not have a center of inversion.
Assisted hopping effects in magnetic impurities and quantum dots are analyzed. The magnitude of the assisted hopping term in a quantum dot in the limit of large level spacing is comparable to other corrections induced by the electron-electron interactions. Assisted hopping leads to differences between conductance peaks associated to the same level, and, when the effect is sufficiently strong, to local pairing correlations.
A simple tight binding model with repulsive interactions is studied. The inclusion of more than one orbital per site leads to assisted hopping effects, and, when the orbitals involved have different symmetries, to an anisotropic superconducting phase. Superconductivity exists for all fillings, and for all values of the on site repulsion.
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