Graphene in external fields

A general discussion of graphene in external electromagnetic field is provided. In general, the formulation is not Lorentz invariant because of Zeeman energy. But it can be restored approxiamtely in the case of strong magnetic field, the condition when quantum Hall effect is observed. Besides obtaining the well-known Hall conductance $\frac{4q^2}{h}(L+1/2)$, we also predict that the sequence of Hall conductance $\frac{4q^2}{h}L$,which contains the newly observed Hall conductance $\frac{4q^2}{h}L$ for $L=0,1$, depending on the filling of Zeeman levels. The energy levels are obtained for general orthogonal constant electric and magnetic field. The second order Dirac equation is derived in applied monochromatic electromagnetic wave, and the major difference between graphene system and convetional Dirac electrons is pointed out.