Screening in gated bilayer graphene via variational calculus

We analyze the response of bilayer graphene to an external transverse electric field using a variational method. A previous attempt to do so in a recent paper by Falkovsky [Phys. Rev. B 80, 113413 (2009)] is shown to be flawed. Our calculation reaffirms the original results obtained by one of us [E. McCann, Phys. Rev. B 74, 161403(R) (2006)] by a different method. Finally, we generalize these original results to describe a dual-gated bilayer graphene device.Comment: 4 pages, 1 figur

The Absence of the Fractional Quantum Hall Effect at High Landau Levels

We compare the energies of the Laughlin liquid and a charge density wave in a weak magnetic field for the upper Landau level filling factors $\nu_N = 1/3$ and $1/5$. The charge density wave period has been optimized and was found to be $\simeq 3R_c$, where $R_c$ is the cyclotron radius. We conclude that the optimal charge density wave is more energetically preferable than the Laughlin liquid for the Landau level numbers $N \ge 2$ at $\nu_N = 1/3$ and for $N \ge 3$ at $\nu_N = 1/5$. This implies that the $1/3$ fractional quantum Hall effect cannot be observed for $N \ge 2$, in agreement with the experiment.Comment: 12 pages, revtex, 2 PostScript figures are applied. Revised and corrected version. Also available at http://www.mnhep.umn.edu/~mfogler

Cyclotron resonance in a two-dimensional electron gas with long-range randomness

We show that the the cyclotron resonance in a two-dimensional electron gas has non-trivial properties if the correlation length of the disorder is larger than the de Broglie wavelength: (a) the lineshape assumes three different forms in strong, intermediate, and weak magnetic fields (b) at the transition from the intermediate to the weak fields the linewidth suddenly collapses due to an explosive growth in the fraction of electrons with a diffusive-type dynamics.Comment: A few typos correcte

Comment on ``Analytic Structure of One-Dimensional Localization Theory: Re-Examining Mott's Law''

The low-frequency conductivity of a disordered Fermi gas in one spatial dimension is governed by the Mott-Berezinskii law $\sigma(\omega) \propto \omega^2 \ln \omega^2$. In a recent Letter [Phys. Rev. Lett. 84, 1760 (2000)] A. O. Gogolin claimed that this law is invalid, challenging our basic understanding of disordered systems and a massive amount of previous theoretical work. We point out two calculational errors in Gogolin's paper. Once we correct them, the Mott-Berezinskii formula is fully recovered. We also present numerical results supporting the Mott-Berezinskii formula but ruling out that of Gogolin.Comment: 1 page, 1 figure, RevTeX