At low energy (close to the Dirac point), clean graphene displays very large and weakly temperature dependent charge mobilities, outperforming any other semiconducting material. These good conduction features result from the very peculiar nature of electronic states (having a pseudospin degree of freedom) which have been theoretically predicted to trigger anomalous transport features such as Klein tunneling [1] or weak antilocalization phenomena [2], which are unique quantum effects to these materials.

An in-depth understanding of the impact of the disorder on graphene transport properties is however of crucial importance not only for fundamental purposes (nature of localization in 2D,..) but also in view of future applications in fields such as nanoelectronics, high-speed devices, sensors, flat displays or photovoltaic devices. When (clean) graphene is deposited onto an oxide substrate, transport properties are expected to be mainly limited by long range scatters either linked to charges trapped in the underneath oxide, mechanical deformations (ripples) frozen during the deposition process or uncontrollable weakly bonded adsorbed impurities [3-5]. Despite a great wealth of academic studies and ab initio calculations, many fundamental issues such as the origin of weak antilocalization in real materials, or the possibility of a metal-insulator transition for massless Dirac fermions remain fiercely debated.

On the other side, the tuning of graphene electronic properties by chemical functionalization could open a new era of solid state electronics based on composite materials [6]. Indeed, chemical functionalization of graphene can be a way to enhance the functionalities or improve the performance of graphene-based devices Severe modifications of the initial sp2-bonded carbon materials by ion irradiation or intentional introduction of sp3 defects also suggest a route to produce strong enough disorder in graphene to tune localization phenomena [7]. In the situation of a nearly complete oxidation of the graphene sheet, the material becomes a sp3 chemical derivative of graphene with sheet resistance several orders of magnitude higher than clean graphene, reaching the MOhm or GOhm regimes. Additionally a strongly invasive hydrogenation treatment of suspended graphene can turn the material into graphane, a true band insulator [8]. 

In addition to these spectacular charge transport properties, graphene-based materials also hold great promises for spintronics devices. Clean graphene nanoribbons were first theoretically predicted to behave as half-metals (carrying a spin current) in the presence of a sufficiently large electric field [9]. An applied transverse electric field was indeed shown to transform the ribbon from a semiconductor with a small gap to a metal with carriers that are 100 percent spin-polarized. The same effect has been predicted by interfacing graphene with a polar material (like a BN sheet), in such a way that the interface dipole makes the role of the electric field [10] The further use of electric or magnetic fields opens the possibility to generate, manipulate, and detect electron spins and spin currents [11,12]. Different ways of increasing the spin correlation length at graphene edges have been further theoretically envisioned by appropriate chemical modification of graphene edges. Similar control of the spin-dependent transport characteristics is regularly proposed and first experimental reports confirm the genuine potential of chemically tuned spin-dependent signals [13], paving the way towards the advent of revolutionary spintronics applications. 

However, much of the theoretical work involving transport in these materials, either involves very simplistic (pi-electron TB or Dirac Hamiltonians), too simplified to produce quantitative predictions for specific functionalizatoins, or they infolve precise ab-initio calculations but limited to small scale defected materials, which make the connection to experiments and real applications elusive.

To investigate in-depth these complex charge and spin transport phenomena there is therefore a crucial need for bridging first principles approaches with mesoscopic transport and device simulation frameworks. Indeed, the local chemical complexity of defected graphene can not be always easily described by simple effective or tight-binding models, without recoursing to extensive structure relaxation and ab initio calculations of resulting electronic and vibrational structures [14]. The large chemical reactivity of graphene based materials also demand particular care and sophisticated calculations in various environment conditions.

Additionally, mesoscopic transport calculations are needed for a realistic inspection of the fundamental (charge and spin) transport properties in disordered materials in low dimension, as well as to explore in-depth the true potential of chemically modified graphene for novel devices functionalities [15,16,17]. This demands for the development of novel order N computational schemes to be implemented in either Kubo or Landauer-Büttiker, Keldysh or similar types of transport methodologies [18].