Engineering quantum anomalous Hall phases with orbital and spin

Combining tight-binding models and first principles calculations, we demonstrate that under external exchange fields, non-zero Chern numbers and nontrivial QAH effect could be induced by on-site spin-orbit coupling (SOC) in buckled honeycomb lattices with $sp$ orbitals. In the Haldane model [1], the occurrence of QAH effect is attributed to complex next nearest neighbor hopping. Detailed analysis of a generic tight-binding models reveals that there exist different mechanisms giving rise to complex hoppings, utilizing both orbital and spin degrees of freedom of electrons on a lattice. Furthermore, it is shown that in Bi/Sb(111) bilayers [2], different topological phases exist as function of the magnitude of SOC and external exchange fields. These phases are characterized using Chern and spin Chern numbers [3] together with transverse charge and spin conductivities. At last, we show that introducing ferromagnetic dopants provides a practical way to induce nontrivial topological phases, whereas the physics is modified due to incompletely filled d states around the Fermi energy.\\[4pt] [1] F.D.M. Haldane, Phys. Rev. Lett. 61, 2015 (1988).\\[0pt] [2] H. Zhang, {\it et al.}, Phys. Rev. B 86, 035104 (2012).\\[0pt] [3] E. Prodan, Phys. Rev. B {\bf 83}, 195119 (2011).