Heavily electron-doped surfaces of Bi$_2$Se$_3$ have been studied by spin and angle resolved photoemission spectroscopy. Upon doping, electrons occupy a series of {bf k}-split pairs of states above the topological surface state. The {bf k}-splitting
originates from the large spin-orbit coupling and results in a Rashba-type behavior, unequivocally demonstrated here via the spin analysis. The spin helicities of the lowest laying Rashba doublet and the adjacent topological surface state alternate in a left-right-left sequence. This spin configuration sets constraints to inter-band scattering channels opened by electron doping. A detailed analysis of the scattering rates suggests that intra-band scattering dominates with the largest effect coming from warping of the Fermi surface.
We have performed photoemission studies of the electronic structure in LiC$_6$ and KC$_8$, a non-superconducting and a superconducting graphite intercalation compound, respectively. We have found that the charge transfer from the intercalant layers t
o graphene layers is larger in KC$_8$ than in LiC$_6$, opposite of what might be expected from their chemical composition. We have also measured the strength of the electron-phonon interaction on the graphene-derived Fermi surface to carbon derived phonons in both materials and found that it follows a universal trend where the coupling strength and superconductivity monotonically increase with the filling of graphene $pi^{ast}$ states. This correlation suggests that both graphene-derived electrons and graphene-derived phonons are crucial for superconductivity in graphite intercalation compounds.
