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Role of electrical field in quantum Hall effect of graphene

The ballistic motion of carriers of graphene in an orthogonal electromagnetic field is investigated to explain Hall conductance of graphene under experimental conditions. With the electrical field, all electronic eigen-states have the same expectation value of the velocity operator, or classically, all carriers move in cycloids with the same average velocity. The magnitude of this velocity is just appropriate to generate the quantized Hall conductance which is in turn exactly independent of the external field. Electrical field changes each Landau level into a bundle of energies, whose overlap in large fields destroys the quantized Hall conductance. As the electrical field tends to the critical point, Landau level expansion occurs. As a result, saturation of the Hall conductance may be observed.