We present both numerical and analytical study of graphene roughness with a crystal structure including $500 \times 500$ atoms. The roughness can effectively result in a random gauge field and has important consequences for its electronic structure. Our results show that its height fluctuations in small scales have scaling behavior with a temperature dependent roughness exponent in the interval of $ 0.6 < \chi < 0.7 $. The correlation function of height fluctuations depends upon temperature with characteristic length scale of $ \approx 90 {\AA}$ (at room temperature). We show that the correlation function of the induced gauge field has a short-range nature with correlation length of about $\simeq 2-3 {\AA}$. We also treat the problem analytically by using the Martin-Siggia-Rose method. The renormalization group flows did not yield any delocalized-localized transition arising from the graphene roughness. Our results are in good agreement with recent experimental observations.Comment: 5 Pages, 5 figure

We show the possibility of inducing an edge charge current by applying time-dependent strain in gapped graphene samples preserving time-reversal symmetry. We demonstrate that this edge current has the same origin as the valley Hall response known to exist in the system.

We study the conductance of disordered graphene superlattices with short-range structural correlations. The system consists of electron-and hole-doped graphenes of various thicknesses, which fluctuate randomly around their mean value. The effect of the randomness on the probability of transmission through the system of various sizes is studied. We show that in a disordered superlattice the quasiparticle that approaches the barrier interface almost perpendicularly transmits through the system. The conductivity of the finite-size system is computed and shown that the conductance vanishes when the sample size becomes very large, whereas for some specific structures the conductance tends to a nonzero value in the thermodynamics limit.PACS numbers: 68.65. Cd, 73.40.Lq I. INTRODUCTIONGraphene, a single atomic layer of graphite, has been successfully produced in experiment 1 , which has resulted in intensive investigations on graphene-based structures, due to the fundamental physics interests that is involved and the promising applications 2 . There are significant current efforts devoted to growing graphene epitaxially 3 by thermal decomposition of silicon carbide (SiC), or by vapor deposition of hydrocarbons on catalytic metallic surfaces, which could later be etched away, leaving graphene on an insulating substrate. The low energy quasiparticle excitations in graphene are linearly dispersing, and are described by Dirac cones at the edges of the first Brillouin zone. The linear energy-momentum dispersion has been confirmed by recent observations 4 . The slope of the linear relation corresponds the Fermi velocity of chiral Dirac electrons in graphene, which plays an essential role in the Landau-Fermi liquid theory 5 and has a direct connection to the experimental measurement.There are some unusual features of graphene, such as the effects of electron-electron interactions on the ground-state properties 6 , anomalous tunneling effect described by the Klein tunneling, the tunneling through a p-n junction 7,8 that follows from chiral band states, and the energy-momentum linear dispersion relation. The Klein tunneling predicts that the chiral massless carrier can pass through a high electrostatic potential barrier with probability one, regardless of the height and width of the barrier at normal incidence, which is in contrast with the conventional nonrelativistic massive carrier tunneling where the transmission probability decays exponentially with the increasing of the barrier hight and would depend on the profile of the barrier. 9,10,11,12 An exciting experimental development is the ability to apply an electric field effect or submicron gate voltage, in order to illustrate graphene p-n junctions. 13 By applying an external gate voltage, the system can be switched from the n-type to the p-type carriers, thereby controlling the electronic properties that give rise to graphene-based nanodevices. Recently, strong evidence for Klein tunneling across potential steps which is steep enough in graphene has been experimentally...

The motion of a C 60 molecule over a graphene sheet at finite temperature is investigated both theoretically and computationally. We show that a graphene sheet generates a van der Waals laterally periodic potential, which directly influences the motion of external objects in its proximity. The translational motion of a C 60 molecule near a graphene sheet is found to be diffusive in the lateral directions. While, in the perpendicular direction, the motion may be described as diffusion in an effective harmonic potential which is determined from the distribution function of the position of the C 60 molecule. We also examine the rotational diffusion of C 60 and show that its motion over the graphene sheet is not a rolling motion.