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A honeycomb lattice system has four types of Dirac electrons corresponding tothe spin and valley degrees of freedom. We consider a state that contains onlyone type of massless electrons and three types of massive ones, which we callthe single Dirac-cone state. We analyze quantum Hall (QH) effects in thisstate. We make a detailed investigation of the Chern and spin-Chern numbers. Wemake clear the origin of unconventional QH effects discovered in graphene. Wealso show that the single Dirac-cone state may have arbitrary large spin-Chernnumbers in magnetic field. Such a state will be generated in antiferromagnetictransition-metal oxides under electric field or silicene with antiferromagneticorder under electric field.

Single Dirac-Cone State and Quantum Hall Effects in Honeycomb Structure