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We consider a modified graphene model under exchange couplings. Variousquantum anomalous phases are known to emerge under uniform or staggeredexchange couplings. We introduce the twist between the orientations of twosublattice exchange couplings, which is useful for examining how suchtopologically nontrivial phases under different types of exchange couplings areconnected to one another. The phase diagrams constructed by the variation ofexchange coupling strengths and twist angles exhibit rich structures ofsuccessive topological transitions. We analyze the emergence of peculiar phasesin terms of the evolution of the energy dispersions. Perturbation schemesapplied to the energy levels turn out to reproduce well phase boundary lines upto moderate values of the twist angle. We also discover two close topologicaltransitions under uniform exchange couplings, which is attributed to theinterplay of the trigonal-warping deformation due to Rashba spin-orbit couplingand the staggered sublattice potential. Finally the implications of Berrycurvature structure and topological excitations in real and pseudo spintextures are discussed.

Topological phase transitions induced by the variation of exchange couplings in graphene