Effect of Rashba splitting on RKKY interaction in topological insulator thin films

In this work we have investigated the effect of Rashba splitting on the RKKY interaction in TI thin film both at finite and zero chemical potential. We find that the spin susceptibility of Rashba materials including TI thin film is strongly dependent on the direction of distance vector. Moreover, we find another term in the off-diagonal terms of the spin-susceptibility tensor which in contrast to the well-known DM-like term is symmetric. We show how one can tune the RKKY interaction by using electric field applied perpendicularly to the surface plane and by small chemical doping giving rise to enhance the RKKY term, drastically. We have presented our results for two different situations, namely inter-surface pairing of magnetic impurities as well as intra-surface one. The behavior of these two situations is completely different which we describe it by mapping the density of states of each surface on the band dispersion.