  A honeycomb lattice system has four types of Dirac electrons corresponding to
the spin and valley degrees of freedom. We consider a state that contains only
one type of massless electrons and three types of massive ones, which we call
the single Dirac-cone state. We analyze quantum Hall (QH) effects in this
state. We make a detailed investigation of the Chern and spin-Chern numbers. We
make clear the origin of unconventional QH effects discovered in graphene. We
also show that the single Dirac-cone state may have arbitrary large spin-Chern
numbers in magnetic field. Such a state will be generated in antiferromagnetic
transition-metal oxides under electric field or silicene with antiferromagnetic
order under electric field.
