Renormalised Intrinsic and Extrinsic Impurity Induced Spin-orbit Scattering in Graphene
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- Institutt for fysikk 
We study the effect of an impurity potential on spin-memory loss in graphene. Various general methods for finding the spin-orbit related effect of a slowly varying impurity potential on a semiconductor have been examined. We have also revisited problems concerning electronic properties and spin relaxation in graphene. To this end, the bandstructure for graphene has been calculated through analytical and computational methods. The following results have been reproduced: Low energy excitations behave like massless relativistic particles with an effective speed of light at roughly 10^6 m/s. Intrinsic spin-orbit coupling splits the bands at the Fermi level. The importance of the $d$ orbitals for this effect is also shown. Extrinsic spin-orbit coupling induced by a perpendicular electric field give rise to a Rashba type Hamiltonian. Our novel results are related to extrinsic effects from an impurity. We have calculated the renormalised impurity induced spin-orbit coupling due to mixing of the conduction bands and the other bands. This renormalisation is at most comparable to the vacuum term, and thus cannot explain the experimental results on spin relaxation.