Quantum Hall effect in ac driven graphene: From the half-integer to the integer case

We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at sigma(xy) = +/-(n + 1/2)4e(2)/h (n is an integer) gets qualitatively changed with the addition of new integer Hall plateaus at sxy = +/- n(4e(2)/h) starting from the edges of the band center regime towards the band center with an increasing ac field. Beyond a critical field strength, a Hall plateau with sigma(xy) = 0 can be realized at the band center, hence fully restoring a conventional integer QHE with particle-hole symmetry. Within a low-energy Hamiltonian for Dirac cones merging, we show a very good agreement with the tight-binding calculations for the Hall plateau transitions. We also obtain the band structure for driven graphene ribbons to provide a further understanding on the appearance of the new Hall plateaus, showing a trivial insulator behavior for the sigma(xy) = 0 state. In the presence of disorder, we numerically study the disorder-induced destruction of the quantum Hall states in a finite driven sample and find that qualitative features known in the undriven disordered case are maintained.