Anomalous Hall effect in rhombohedral graphene

Motivated by recent experiments on rhombohedral stacked multilayer graphene and the observation of the anomalous Hall effect in a spontaneous spin-valley-polarized quarter-metal state, we calculate the anomalous Hall conductivity for this system in the presence of two types of impurities: weak and dense as well as sparse and strong. Our calculation of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>σ</a:mi> <a:mrow> <a:mi>x</a:mi> <a:mi>y</a:mi> </a:mrow> </a:msub> </a:math> is based on the Kubo-Streda diagrammatic approach. In a model with Gaussian disorder applicable to weak dense impurities, this involves all noncrossing diagrams (intrinsic, side-jump and Gaussian skew-scattering contributions) and additionally, diagrams with two intersecting impurities, X and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi mathvariant="normal">Ψ</b:mi> </b:math> , representing diffractive skew-scattering processes. A “Mercedes star” diagram (non-Gaussian skew scattering) is furthermore included to treat in the case of strong, sparse impurities. We supplement our asymptotically exact analytical solutions for an isotropic model without warping effects by seminumerical calculations accounting perturbatively for warping, which plays a crucial role in the low-energy band structure.