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

Kai-He Ding,1 Lih-King Lim,2,3,* Gang Su,4 and Zheng-Yu Weng3,5

1Department of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410076, P. R. China

2Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, P. R. China

3Institute for Advanced Study, Tsinghua University, Beijing 100084, P. R. China

4Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, School of Physics, University of Chinese Academy of Science, Beijing 100049, P. R. China

5Collaborative Innovation Center of Quantum Matter, Tsinghua University, Beijing 100084, P. R. China

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 σxy = ±(n + 1/2)4e2/h (n is an integer) gets qualitatively changed with the addition of new integer Hall plateaus at σxy = ±n(4e2/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 σxy = 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 σxy = 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.