We investigate the electronic transport properties of unbiased and biased bilayer graphene nanoribbon in n-p and n-n junctions subject to a perpendicular magnetic field. Using the non-equilibrium Greens function method and the Landauer-B{u}ttiker for
malism, the conductance is studied for the cases of clean, on-site, and edge disordered bilayer graphene. We show that the lowest Hall plateau remains unchanged in the presence of disorder, whereas asymmetry destroys both the plateaus and conductance quantization. In addition, we show that disorder induces an enhancement of the conductance in the n-p region in the presence of magnetic fields. Finally, we show that the equilibration of quantum Hall edge states between distinctively doped regions causes Hall plateaus to appear in the regime of complete mode mixing.
The amount of rippling in graphene sheets is related to the interactions with the substrate or with the suspending structure. Here, we report on an irreversibility in the response to forces that act on suspended graphene sheets. This may explain why
one always observes a ripple structure on suspended graphene. We show that a compression-relaxation mechanism produces static ripples on graphene sheets and determine a peculiar temperature $T_c$, such that for $T<T_c$ the free-energy of the rippled graphene is smaller than that of roughened graphene. We also show that $T_c$ depends on the structural parameters and increases with increasing sample size.
The motion of a C60 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 motio
n of external objects in its proximity. The translational motion of a C60 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 C60 molecule. We also examine the rotational diffusion of C60 and show that its motion over the graphene sheet is not a rolling motion.
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.
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. O
ur 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.
