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We study the effects of the long-range disorder potential and warping on the conductivity and mobility of graphene ribbons using the Landauer formalism and the tight-binding p-orbital Hamiltonian. We demonstrate that as the length of the structure increases the system undergoes a transition from the ballistic to the diffusive regime. This is reflected in the calculated electron density dependencies of the conductivity and the mobility. In particular, we show that the mobility of graphene ribbons varies as mu(n) n^(-lambda), with 0<lambda<0.5. The exponent lambda depends on the length of the system with lambda=0.5 corresponding to short structures in the ballistic regime, whereas the diffusive regime lambda=0 (when the mobility is independent on the electron density) is reached for sufficiently long structures. Our results can be used for the interpretation of experimental data when the value of lambda can be used to distinguish the transport regime of the system (i.e. ballistic, quasi-ballistic or diffusive). Based on our findings we discuss available experimental results.
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We calculate the carrier density dependent ground state properties of graphene in the presence of random charged impurities in the substrate taking into account disorder and interaction effects non-perturbatively on an equal footing in a self-consistent theoretical formalism. We provide detailed quantitative results on the dependence of the disorder-induced spatially inhomogeneous two-dimensional carrier density distribution on the external gate bias, the impurity density, and the impurity location. We find that the interplay between disorder and interaction is strong, particularly at lower impurity densities. We show that for the currently available typical graphene samples, inhomogeneity dominates graphene physics at low ($lesssim 10^{12}$ cm$^{-2}$) carrier density with the density fluctuations becoming larger than the average density.
Zig-zag edge graphene ribbons grown on 6H-SiC facets are ballistic conductors. It has been assumed that zig-zag graphene ribbons grown on 4H-SiC would also be ballistic. However, in this work we show that SiC polytype matters; ballistic graphene ribbons only grow on 6H SiC. 4H and 4H-passivated ribbons are diffusive conductors. Detailed photoemmision and microscopy studies show that 6H-SiC sidewalls zig-zag ribbons are metallic with a pair of n-doped edge states associated with asymmetric edge terminations, In contrast, 4H-SiC zig-zag ribbons are strongly bonded to the SiC; severely distorting the ribbons $pi$-bands. $text{H}_2$-passivation of the 4H ribbons returns them to a metallic state but show no evidence of edge states.
Improved fabrication techniques have enabled the possibility of ballistic transport and unprecedented spin manipulation in ultraclean graphene devices. Spin transport in graphene is typically probed in a nonlocal spin valve and is analyzed using spin diffusion theory, but this theory is not necessarily applicable when charge transport becomes ballistic or when the spin diffusion length is exceptionally long. Here, we study these regimes by performing quantum simulations of graphene nonlocal spin valves. We find that conventional spin diffusion theory fails to capture the crossover to the ballistic regime as well as the limit of long spin diffusion length. We show that the latter can be described by an extension of the current theoretical framework. Finally, by covering the whole range of spin dynamics, our study opens a new perspective to predict and scrutinize spin transport in graphene and other two-dimensional material-based ultraclean devices.
We investigate the diffusive electron-transport properties of charge-doped graphene ribbons and nanoribbons with imperfect edges. We consider different regimes of edge scattering, ranging from wide graphene ribbons with (partially) diffusive edge scattering to ribbons with large width variations and nanoribbons with atomistic edge roughness. For the latter, we introduce an approach based on pseudopotentials, allowing for an atomistic treatment of the band structure and the scattering potential, on the self-consistent solution of the Boltzmann transport equation within the relaxation-time approximation and taking into account the edge-roughness properties and statistics. The resulting resistivity depends strongly on the ribbon orientation, with zigzag (armchair) ribbons showing the smallest (largest) resistivity and intermediate ribbon orientations exhibiting intermediate resistivity values. The results also show clear resistivity peaks, corresponding to peaks in the density of states due to the confinement-induced subband quantization, except for armchair-edge ribbons that show a very strong width dependence because of their claromatic behavior. Furthermore, we identify a strong interplay between the relative position of the two valleys of graphene along the transport direction, the correlation profile of the atomistic edge roughness, and the chiral valley modes, leading to a peculiar strongly suppressed resistivity regime, most pronounced for the zigzag orientation.
On a high-mobility 2D electron gas we have observed, in strong magnetic fields (omega_{c} tau > 1), a parabolic negative magnetoresistance caused by electron-electron interactions in the regime of k_{B} T tau / hbar ~ 1, which is the transition from the diffusive to the ballistic regime. From the temperature dependence of this magnetoresistance the interaction correction to the conductivity delta sigma_{xx}^{ee}(T) is obtained in the situation of a long-range fluctuation potential and strong magnetic field. The results are compared with predictions of the new theory of interaction-induced magnetoresistance.
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