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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 $sigma_{xy} = pm(n + 1/2)4e^2/h$ ($n$ is an integer) gets qualitatively changed with the addition of new integer Hall plateaus at $sigma_{xy} = pm n(4e^2/h)$ 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 restoring fully 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.
The quantum Hall effect, with a Berrys phase of $pi$ is demonstrated here on a single graphene layer grown on the C-face of 4H silicon carbide. The mobility is $sim$ 20,000 cm$^2$/V$cdot$s at 4 K and ~15,000 cm$^2$/V$cdot$s at 300 K despite contamina
In this review the physics of Pfaffian paired states, in the context of fractional quantum Hall effect, is discussed using field-theoretical approaches. The Pfaffian states are prime examples of topological ($p$-wave) Cooper pairing and are character
We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We then establ
Fractional quantum Hall states at half-integer filling factors have been observed in many systems beyond the $5/2$ and $7/2$ plateaus in GaAs quantum wells. This includes bilayer states in GaAs, several half-integer plateaus in ZnO-based heterostruct
We report the observation of the quantized Hall effect in suspended graphene probed with a two-terminal lead geometry. The failure of earlier Hall-bar measurements is discussed and attributed to the placement of voltage probes in mesoscopic samples.