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

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

Dynamics of disordered quantum Hall crystals

Charge density waves are thought to be common in two-dimensional electron systems in quantizing magnetic fields. Such phases are formed by the quasiparticles of the topmost occupied Landau level when it is partially filled. One class of charge density wave phases can be described as electron solids. In weak magnetic fields (at high Landau levels) solids with many particles per unit cell - bubble phases - predominate. In strong magnetic fields (at the lowest Landau level) only crystals with one particle per unit cell - Wigner crystals - can form. Experimental identification of these phases is facilitated by the fact that even a weak disorder influences their dc and ac magnetotransport in a very specific way. In the ac domain, a range of frequencies appears where the electromagnetic response is dominated by magnetophonon collective modes. The effect of disorder is to localize the collective modes and to create an inhomogeneously broadened absorption line, the pinning mode. In recent microwave experiments pinning modes have been discovered both at the lowest and at high Landau levels. We present the theory of the pinning mode for a classical two-dimensional electron crystal collectively pinned by weak impurities. We show that long-range Coulomb interaction causes a dramatic line narrowing, in qualitative agreement with the experiments.Comment: 6 pages, 3 figures. To be presented at EP2DS-15, Nara, Japan. One typo correcte

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

Neutrality point of graphene with coplanar charged impurities

The ground-state and the transport properties of graphene subject to the potential of in-plane charged impurities are studied. The screening of the impurity potential is shown to be nonlinear, producing a fractal structure of electron and hole puddles. Statistical properties of this density distribution as well as the charge compressibility of the system are calculated in the leading-log approximation. The conductivity depends logarithmically on $\alpha$, the dimensionless strength of the Coulomb interaction. The theory is asymptotically exact when $\alpha$ is small, which is the case for graphene on a substrate with a high dielectric constant.Comment: (v3) 4 pages main paper, 2 pages supplementary info, no figure