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We investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities in both single layer and Bernal stacked bilayer graphene, finding a number of striking anomalies in the temperature dependence of this interaction. In undoped single layer graphene the strength of the RKKY interaction for substitutional impurities anomalously increases upon increasing temperature, an effect that persists up to and beyond room temperature. For impurities intercalated in the Bernal stacked bilayer and a doping that places the chemical potential near the antibonding band edge, a qualitative change of the RKKY interaction with temperature occurs: a low-temperature oscillatory interaction develops into a high-temperature antiferromagnetic coupling, accompanied by an overall increase of the interaction strength. The origin of the temperature anomalies can be traced back to specific features of the density of states: the vanishing density of states at the apex of the Dirac cone in single layer graphene, and the "kink" in the density of states at the antibonding band edge in the case of the Bernal bilayer.

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Deploying an analytical atomistic model of the bulk band structure of the IV-VI semiconductors we connect the spin structure of the topological surface state to the crystal field and spin orbit coupling parameters of the bulk material. While the Dirac-Weyl (or equivalently, Rashba) type topological surface state is often assumed universal, we show that the physics of the surface state is strikingly non-universal. To see this explicitly we calculate the RKKY interaction, which may be viewed as a probe of this surface state spin structure, finding its qualitative form depends on the values the bulk spin-orbit and crystal field parameters take. This opens the way to tune the spin interaction on the surface of a IV-VI topological insulator by, for instance varying the composition of the IV-VI ternary compounds, as well as highlighting the importance of the connection between bulk and surface physics in topological insulators. arXiv:1711.10760v1 [cond-mat.mes-hall]

Weak topological insulators possess a symmetry related set of Dirac-Weyl cones in the surface Brillouin zone, implying misorientation between the principle axis of the low energy manifold of the bulk and the surface normal. We show that this feature of weak topological insulators comes with a hidden richness of surface spin textures, and that by misorientation a helical texture can become an unusual hyperbolic spin texture. We illustrate this effect by comparison of the M -point and Γ-point Dirac-Weyl cones on the (111) surface of the crystalline topological insulator SnTe.