We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in 1+1 and 2+1 dimensions using a Euler discretization scheme and the replacement of (nablah)(2) by exponentially decreasing functions of that quantity to suppress instabilities. When applied to the equation in 1+1 dimensions, the method of instability control provides values of scaling amplitudes consistent with exactly known results, in contrast to the deviations generated by the original scheme. In 2+1 dimensions, we spanned a range of the model parameters where transients with Edwards-Wilkinson or random growth are not observed, in box sizes 8< or =L< or =128 . We obtain a roughness exponent of 0.37< or =alpha< or =0.40 and steady state height distributions with skewness S=0.25+/-0.01 and kurtosis Q=0.15+/-0.1 . These estimates are obtained after extrapolations to the large L limit, which is necessary due to significant finite-size effects in the estimates of effective exponents and height distributions. On the other hand, the steady state roughness distributions show weak scaling corrections and evidence of stretched exponential tails. These results confirm previous estimates from lattice models, showing their reliability as representatives of the KPZ class.

We study the emergence of strongly correlated states and Kondo physics in disordered graphene. Diluted short range disorder gives rise to localized midgap states at the vicinity of the system charge neutrality point. We show that long-range disorder, ubiquitous in graphene, allows for the coupling of these localized states to an effective (disorder averaged) metallic band. The system is described by an Anderson-like model. We use the numerical renormalization group (NRG) method to study the distributions of Kondo temperatures $P(T_K)$. The results show that disorder can lead to long logarithmic tails in $P(T_K)$, consistent with a quantum Griffiths phase.Comment: Published version + Supp. Materia

Vacancies in graphene have been proposed to give rise to π-like magnetism in carbon materials, a conjecture which has been supported by recent experimental evidence. A key element in this "vacancy magnetism" is the formation of magnetic moments in vacancy-induced electronic states. In this work we compute the charging energy U of a single-vacancy generated localized state for bulk graphene and graphene ribbons. We use a tight-binding model to calculate the dependency of the charging energy U on the amplitudes of the localized wave function on the graphene lattice sites. We show that for bulk graphene U scales with the system size L as (ln L) −2 , confirming the predictions in the literature, based on heuristic arguments. In contrast, we find that for realistic system sizes U is of the order of eV, a value that is orders of magnitude higher than the previously reported estimates. Finally, when edges are considered, we show that U is very sensitive to the vacancy position with respect to the graphene flake boundaries. In the case of armchair nanoribbons, we find a strong enhancement of U in certain vacancy positions as compared to the value for vacancies in bulk graphene.

We study the spin relaxation in graphene due to magnetic moments induced by defects. We propose and employ in our studies a microscopic model that describes magnetic impurity scattering processes mediated by charge puddles. This model incorporates the spin texture related to the defect-induced state. We calibrate our model parameters using experimentally-inferred values. The results we obtain for the spin relaxation times are in very good agreement with experimental findings. Our study leads to a comprehensive explanation for the short spin relaxation times reported in the experimental literature. We also propose a new interpretation for the puzzling experimental observation of enhanced spin relaxation times in hydrogenated graphene samples in terms of a combined effect due to disorder configurations that lead to an increased coupling to the magnetic moments and the tunability of the defect-induced π-like magnetism in graphene.