Electronic localization in two dimensions

By an improved scaling analysis, we suggest that there may appear two possibilities concerning the electronic localization in two dimensional random media. The first is that all electronic states are localized in two dimensions, as already conjectured previously. The second possibility is that the electronic behaviors in two and three dimensional random systems are similar, in agreement with a recent calculation based on a direct calculation of the conductance with the use of the Kubo formula. In this case, non-localized states is possible in two dimensions, and possess some peculiar properties. A few predictions are proposed. Moreover, the present analysis seems accommodating results from previous scaling analysis.Comment: 6 pages, 2 figure

Localization of non-interacting electrons in thin layered disordered systems

Localization of electronic states in disordered thin layered systems with b layers is studied within the Anderson model of localization using the transfer-matrix method and finite-size scaling of the inverse of the smallest Lyapunov exponent. The results support the one-parameter scaling hypothesis for disorder strengths W studied and b=1,...,6. The obtained results for the localization length are in good agreement with both the analytical results of the self-consistent theory of localization and the numerical scaling studies of the two-dimensional Anderson model. The localization length near the band center grows exponentially with b for fixed W but no localization-delocalization transition takes place.Comment: 6 pages, 5 figure

On electron (anti)localization in graphene

We discuss localization properties of the Dirac-like electronic states in monolayers of graphite. In the framework of a general disorder model, we identify the conditions under which such standard localization effects as logarithmic temperature-dependent conductivity corrections appear to be strongly suppressed, as compared to the case of a two-dimensional electron gas with parabolic dispersion, in agreement with recent experimental observations.Comment: Latex, no figure

Impurities and electronic localization in graphene bilayers

We analyze the electronic properties of bilayer graphene with Bernal stacking and a low concentration of adatoms. Assuming that the host bilayer lies on top of a substrate, we consider the case where impurities are adsorbed only on the upper layer. We describe non-magnetic impurities as a single orbital hybridized with carbon's pz states. The effect of impurity doping on the local density of states with and without a gated electric field perpendicular to the layers is analyzed. We look for Anderson localization in the different regimes and estimate the localization length. In the biased system, the field induced gap is partially filled by strongly localized impurity states. Interestingly, the structure, distribution and localization length of these states depend on the field polarization.Comment: 7 pages, 6 figure

Delocalization of tightly bound excitons in disordered systems

The localization length of a low energy tightly bound electron-hole pair (excitons) is calculated by exact diagonalization for small interacting disordered systems. The exciton localization length (which corresponds to the thermal electronic conductance) is strongly enhanced by electron-electron interactions, while the localization length (pertaining to the charge conductance) is only slightly enhanced. This shows that the two particle delocalization mechanism widely discussed for the electron pair case is more efficient close to the Fermi energy for an electron-hole pair. The relevance to experiment is also discussed.Comment: 10 pages, 2 figures - old version was posted by mistak

Dirac fermions in a power-law-correlated random vector potential

We study localization properties of two-dimensional Dirac fermions subject to a power-law-correlated random vector potential describing, e.g., the effect of "ripples" in graphene. By using a variety of techniques (low-order perturbation theory, self-consistent Born approximation, replicas, and supersymmetry) we make a case for a possible complete localization of all the electronic states and compute the density of states.Comment: Latex, 4+ page