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We study charge transport in one-dimensional graphene superlattices created by applying layered periodic and disordered potentials. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the direction perpendicular to the layers, the eigenstates in a disordered sample are delocalized for all energies and provide a minimal non-zero conductivity, which cannot be destroyed by disorder, no matter how strong this is. However, along with extended states, there exist discrete sets of angles and energies with exponentially localized eigenfunctions (disorder-induced resonances). It is shown that, depending on the type of the unperturbed system, the disorder could either suppress or enhance the transmission. Most remarkable properties of the transmission have been found in graphene systems built of alternating p-n and n-p junctions. This transmission has anomalously narrow angular spectrum and, surprisingly, in some range of directions it is practically independent of the amplitude of fluctuations of the potential. Owing to these features, such samples could be used as building blocks in tunable electronic circuits. To better understand the physical implications of the results presented here, most of our results have been contrasted with those for analogous wave systems. Along with similarities, a number of quite surprising differences have been found.
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We investigate the conductivity $sigma$ of graphene nanoribbons with zigzag edges as a function of Fermi energy $E_F$ in the presence of the impurities with different potential range. The dependence of $sigma(E_F)$ displays four different types of behavior, classified to different regimes of length scales decided by the impurity potential range and its density. Particularly, low density of long range impurities results in an extremely low conductance compared to the ballistic value, a linear dependence of $sigma(E_F)$ and a wide dip near the Dirac point, due to the special properties of long range potential and edge states. These behaviors agree well with the results from a recent experiment by Miao emph{et al.} (to appear in Science).
We report measurements of disordered graphene probed by both a high electric field and a high magnetic field. By apply a high source-drain voltage Vsd, we are able to study the current-voltage relation I-Vsd of our device. With increasing Vsd, a crossover from the linear I-Vsd regime to the non-linear one, and eventually to activationless-hopping transport occurs. In the activationless-hopping regime, the importance of Coulomb interactions between charged carriers is demonstrated. Moreover, we show that delocalization of carriers which are strongly localized at low T and at small Vsd occurs with the presence of high electric field and perpendicular magnetic field..
We describe the weak localization correction to conductivity in ultra-thin graphene films, taking into account disorder scattering and the influence of trigonal warping of the Fermi surface. A possible manifestation of the chiral nature of electrons in the localization properties is hampered by trigonal warping, resulting in a suppression of the weak anti-localization effect in monolayer graphene and of weak localization in bilayer graphene. Intervalley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore weak localization resulting in negative magnetoresistance in both materials.
We present a magneto-transport study of graphene samples into which a mild disorder was introduced by exposure to ozone. Unlike the conductivity of pristine graphene, the conductivity of graphene samples exposed to ozone becomes very sensitive to temperature: it decreases by more than 3 orders of magnitude between 100K and 1K. By varying either an external gate voltage or temperature, we continuously tune the transport properties from the weak to the strong localization regime. We show that the transition occurs as the phase coherence length becomes comparable to the localization length. We also highlight the important role of disorder-enhanced electron-electron interaction on the resistivity.
A transfer matrix approach is used to study the electronic transport in graphene superlattices with long-range correlated barrier spacements. By considering the low-energy electronic excitations as massless Dirac fermions, we compute by transmission spectra of graphene superlattices with potential barriers having spacements randomly distributed with long-range correlations governed by a power-law spectral density $S(k)propto 1/k^{alpha}$. We show that at large incidence angles, the correlations in the disorder distribution do not play a significant role in the electronic transmission. However, long-range correlations suppress the Anderson localization as normal incidence is approached and a band of transmitting modes sets up reminiscent of Klein tunneling.
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