Influence of correlated impurities on conductivity of graphene sheets: Time-dependent real-space Kubo approach

Abstract

Numerical calculations of the conductivity of graphene sheets with random and correlated distributions of disorders have been performed using the time-dependent real-space Kubo formalism. The disorder was modeled by the long-range Gaussian potential describing screened charged impurities and by the short-range potential describing neutral adatoms both in the weak and strong scattering regimes. Our central result is that correlation in the spatial distribution for the strong short-range scatterers and for the long-range Gaussian potential do not lead to any enhancement of the conductivity in comparison to the uncorrelated case. Our results strongly indicate that the temperature enhancement of the conductivity reported in the recent study [J. Yan and M. S. Fuhrer, Phys. Rev. Lett. 107, 206601 (2011)] and attributed to the effect of dopant correlations was most likely caused by other factors not related to the correlations in the scattering potential.

Charge and Spin Transport in Disordered Graphene-Based Materials

“…Second, a similar increase of the Dirac point conductivity with defect density has been also reported in the diffusive regime of two-dimensional disordered graphene in the presence of vacancies or adatoms [119,102]. These results contrast with the semiclassical conductivity found with the Boltzmann approach [125,35,126,127,128], and suggest the absence of quantum interferences and localization effects observed for other types of disorder [72,129,130]. Finally, transport experiments in intentionally damaged graphene also report on puzzling conductivity fingerprints, whose physical origin remains to be fully understood [131,132].…”

“…Scaling analysis (ξ(E) = ℓ e (E) exp(πhσ sc (E)/2e 2 ) [114]) reveals that ξ ≃ 1 − 10 µm over a large energy window around the charge neutrality point. This contrasts with the values (on the order of 10 nm) obtained for graphene structures with ∼ 1% structural defects, strongly bonded adatoms, or other types of short range impurities [72,129]. Finally, we move on to the charge carrier mobility µ(n) (Fig.…”

“…To investigate the various transport regimes, two complementary approaches are used. For studying two-dimensional (bulk) disordered graphene, real-space quantum wave packet dynamics and Kubo conductivity are calculated [72,99,136,137,129,4].…”

Conductivity of epitaxial and CVD graphene with correlated line defects

“…3 This conclusion was based on the semi-classical predictions relying on the standard Boltzmann approach within the Born approximation. 4 At the same time, numerical calculations within the time-dependent real-space KuboGreenwood formalism showed 5 that correlation in the spatial distribution of short-and long-ranged point defects do not lead to any enhancement of the conductivity in comparison to the uncorrelated case.…”

“…We do this numerically, utilizing the quantum mechanical time-dependent real-space Kubo method 5,19,[22][23][24][25][26][27] allowing us to study graphene sheets approaching the realistic dimensions of millions of atoms.…”