Ultrathin epitaxial graphite was grown on single-crystal silicon carbide by vacuum graphitization. The material can be patterned using standard nanolithography methods. The transport properties, which are closely related to those of carbon nanotubes, are dominated by the single epitaxial graphene layer at the silicon carbide interface and reveal the Dirac nature of the charge carriers. Patterned structures show quantum confinement of electrons and phase coherence lengths beyond 1 micrometer at 4 kelvin, with mobilities exceeding 2.5 square meters per volt-second. All-graphene electronically coherent devices and device architectures are envisaged.

We study the electronic structure of two Dirac electron gazes coupled by a periodic Hamiltonian such as it appears in rotated graphene bilayers. Ab initio and tight-binding approaches are combined and show that the spatially periodic coupling between the two Dirac electron gazes can renormalize strongly their velocity. We investigate in particular small angles of rotation and show that the velocity tends to zero in this limit. The localization is confirmed by an analysis of the eigenstates which are localized essentially in the AA zones of the Moiré patterns.

Charge transport in crystalline organic semiconductors is intrinsically limited by the presence of large thermal molecular motions, which are a direct consequence of the weak van der Waals inter-molecular interactions. These lead to an original regime of transport called transient localization, sharing features of both localized and itinerant electron systems. After a brief review of experimental observations that pose a challenge to the theory, we concentrate on a commonly studied model which describes the interaction of the charge carriers with inter-molecular vibrations. We present different theoretical approaches that have been applied to the problem in the past, and then turn to more modern approaches that are able to capture the key microscopic phenomenon at the origin of the puzzling experimental observations, i.e. the quantum localization of the electronic wavefuntion at timescales shorter than the typical molecular motions. We describe in particular a relaxation time approximation which clarifies how the transient localization due to dynamical molecular motions relates to the Anderson localization realized for static disorder, and allows us to devise strategies to improve the mobility of actual compounds. The relevance of the transient localization scenario to other classes of systems is briefly discussed.

Rotated graphene multilayers form a new class of graphene related systems with electronic properties that drastically depend on the rotation angles. It has been shown that bilayers behave like two isolated graphene planes for large rotation angles. For smaller angles, states in the Dirac cones belonging to the two layers interact resulting in the appearance of two van Hove singularities. States become localised as the rotation angle decreases and the two van Hove singularities merge into one peak at the Dirac energy. Here we go further and consider bilayers with very small rotation angles. In this case, well defined regions of AA stacking exist in the bilayer supercell and we show that states are confined in these regions for energies in the [-\gamma_t, +\gamma_t] range with \gamma_t the interplane mean interaction. As a consequence, the local densities of states show discrete peaks for energies different from the Dirac energy.Comment: 8 page

The charge mobility of molecular semiconductors is limited by the large fluctuation of intermolecular transfer integrals, often referred to as off-diagonal dynamic disorder, which causes transient localization of the carriers' eigenstates. Using a recently developed theoretical framework, we show here that the electronic structure of the molecular crystals determines its sensitivity to intermolecular fluctuations. We build a map of the transient localization lengths of high-mobility molecular semiconductors to identify what patterns of nearest-neighbour transfer integrals in the two-dimensional (2D) high-mobility plane protect the semiconductor from the effect of dynamic disorder and yield larger mobility. Such a map helps rationalizing the transport properties of the whole family of molecular semiconductors and is also used to demonstrate why common textbook approaches fail in describing this important class of materials. These results can be used to rapidly screen many compounds and design new ones with optimal transport characteristics.

A relation derived from the Kubo formula shows that optical conductivity measurements below the gap frequency in doped semiconductors can be used to probe directly the time-dependent quantum dynamics of charge carriers. This allows to extract fundamental quantities such as the elastic and inelastic scattering rates, as well as the localization length in disordered systems. When applied to crystalline organic semiconductors, an incipient electron localization caused by large dynamical lattice disorder is unveiled, implying a breakdown of semiclassical transport.Comment: Revised version, to appear in Phys. Rev. B Rapid Communication

We develop a new real-space method which allows to evaluate the Kubo-Greenwood formula for dc-conductivity of independent electrons in a static potential. We apply it to a numerical study of propagation modes in 3 dimensional quasiperiodic systems. These modes are strikingly different from those of periodic ones, with regard to the effect of disorder. In particular for Fermi energies in pseudo-gaps the conductivity can be stable or can even increase when disorder increases.

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