We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

This article reviews the electronic and transport properties of carbon nanotubes. The focus is mainly theoretical, but when appropriate the relation with experimental results is mentioned. While simple band-folding arguments will be invoked to rationalize how the metallic or semiconducting character of nanotubes is inferred from their topological structure, more sophisticated tight-binding and ab initio treatments will be introduced to discuss more subtle physical effects, such as those induced by curvature, tube-tube interactions, or topological defects. The same approach will be followed for transport properties. The fundamental aspects of conduction regimes and transport length scales will be presented using simple models of disorder, with the derivation of a few analytic results concerning specific situations of short-and long-range static perturbations. Further, the latest developments in semiempirical or ab initio simulations aimed at exploring the effect of realistic static scatterers ͑chemical impurities, adsorbed molecules, etc.͒ or inelastic electron-phonon interactions will be emphasized. Finally, specific issues, going beyond the noninteracting electron model, will be addressed, including excitonic effects in optical experiments, the Coulomb-blockade regime, and the Luttinger liquid, charge density waves, or superconducting transition.

We report on a numerical study of electronic transport in chemically doped 2D graphene materials. By using ab initio calculations, a self-consistent scattering potential is derived for boron and nitrogen substitutions, and a fully quantum-mechanical Kubo-Greenwood approach is used to evaluate the resulting charge mobilities and conductivities of systems with impurity concentration ranging within [0.5, 4.0]%. Even for a doping concentration as large as 4.0%, the conduction is marginally affected by quantum interference effects, preserving therefore remarkable transport properties, even down to the zero temperature limit. As a result of the chemical doping, electron-hole mobilities and conductivities are shown to become asymmetric with respect to the Dirac point.

We report on first-principles calculations of spin-dependent properties in graphene induced by its interaction with a nearby magnetic insulator (europium oxide, EuO). The magnetic proximity effect results in spin polarization of graphene π orbitals by up to 24%, together with a large exchange-splitting band gap of about 36 meV. The position of the Dirac cone is further shown to depend strongly on the graphene-EuO interlayer. These findings point toward the possible engineering of spin gating by the proximity effect at a relatively high temperature, which stands as a hallmark for future all-spin information processing technologies.

Two-dimensional graphene, carbon nanotubes, and graphene nanoribbons represent a novel class of low dimensional materials that could serve as building blocks for future carbon-based nanoelectronics. Although these systems share a similar underlying electronic structure, whose exact details depend on confi nement effects, crucial differences emerge when disorder comes into play. In this review, we consider the transport properties of these materials, with particular emphasis on the case of graphene nanoribbons. After summarizing the electronic and transport properties of defect-free systems, we focus on the effects of a model disorder potential (Anderson-type), and illustrate how transport properties are sensitive to the underlying symmetry. We provide analytical expressions for the elastic mean free path of carbon nanotubes and graphene nanoribbons, and discuss the onset of weak and strong localization regimes, which are genuinely dependent on the transport dimensionality. We also consider the effects of edge disorder and roughness for graphene nanoribbons in relation to their armchair or zigzag orientation.

No abstract

We report on fundamental aspects of spin dynamics in heterostructures of graphene and transition metal dichalcogenides (TMDCs). By using realistic models derived from first principles we compute the spin lifetime anisotropy, defined as the ratio of lifetimes for spins pointing out of the graphene plane to those pointing in the plane. We find that the anisotropy can reach values of tens to hundreds, which is unprecedented for typical 2D systems with spin-orbit coupling and indicates a qualitatively new regime of spin relaxation. This behavior is mediated by spin-valley locking, which is strongly imprinted onto graphene by TMDCs. Our results indicate that this giant spin lifetime anisotropy can serve as an experimental signature of materials with strong spin-valley locking, including graphene/TMDC heterostructures and TMDCs themselves. Additionally, materials with giant spin lifetime anisotropy can provide an exciting platform for manipulating the valley and spin degrees of freedom, and for designing novel spintronic devices. [3,4], where the combined system might be engineered for specific applications [5] or might enable the exploration of new phenomena [6,7]. In the field of spintronics, graphene has exceptional charge transport properties but weak spin-orbit coupling (SOC) on the order of 10 µeV [8], which makes it ideal for long-distance spin transport [9-11] but ineffective for generating or manipulating spin currents. To advance towards spin manipulation, recent work has focused on heterostructures of graphene and magnetic insulators [12][13][14][15][16] or strong SOC materials such as transition metal dichalcogenides (TMDCs) and topological insulators [17][18][19]. The SOC induced in graphene by a TMDC could enable phenomena such as topological edge states [20] or the spin Hall effect [21][22][23].To this end, a variety of recent experiments have explored spin transport in graphene/TMDC heterostructures [21,[24][25][26][27][28][29]. Magnetotransport measurements revealed that graphene in contact with WS 2 exhibits a large weak antilocalization (WAL) peak, revealing a strong SOC induced by proximity effects [24][25][26]30]. Fits to the magnetoconductance yielded spin lifetimes τ s ≈ 5 ps, which is two to three orders of magnitude lower than graphene on traditional substrates [10,31]. It was later asserted that after the removal of a temperatureindependent background, τ s becomes at most only a few hundred femtoseconds [26]. Nonlocal Hanle measurements, meanwhile, have revealed spin lifetimes up to a few tens of picoseconds [27][28][29] that can be tuned by a back gate [28,29]. Finally, charge transport measure-

We present first-principles calculations of quantum transport in chemically doped graphene nanoribbons with a width of up to 4 nm. The presence of boron and nitrogen impurities is shown to yield resonant backscattering, whose features are strongly dependent on the symmetry and the width of the ribbon, as well as the position of the dopants. Full suppression of backscattering is obtained on the pi-pi* plateau when the impurity preserves the mirror symmetry of armchair ribbons. Further, an unusual acceptor-donor transition is observed in zigzag ribbons. These unconventional doping effects could be used to design novel types of switching devices.