# Computational Atomistic Modeling in Carbon Flatland and Other 2D Nanomaterials
## 2 Electronic Transport in Polycrystalline Graphene  
Although graphene was first isolated by mechanical exfoliation [20], it is currently synthesized for the most part by chemical vapor deposition (CVD) techniques. This approach is presently by far the most viable and industry-compatible production method [23; 24]. Importantly, CVD yields polycrystalline graphene (PG) where single-crystal domains are separated by graphene grain boundaries (GBs) of irregular shapes. Grains have a roughness comparable to the substrate and a lateral size ranging from a few hundred nanometers to several centimeters [25]. At the grains interface, topological defects accommodate for the lattice misorientation between domains. Those GBs consist of non-hexagonal rings (mostly pentagon-heptagon pairs) randomly distributed along the interface [26; 27]. It was revealed by scanning probe microscopy that such extended structural defects induce major perturbations in the electronic structure of graphene [28; 29]. The transport of charge carriers is degraded on the one hand by structural defects acting as scattering sites [30; 31; 32] and on the other hand by electrical potential barriers formed at GBs which tend to be negatively-doped (_n_-doped) [33; 34]. A strong correlation was demonstrated between the quality and the resistivity of GBs [30; 32; 35]. Macroscopically, the carrier mobility of wafer-scale graphene is drastically limited by GBs [36; 37; 38]. Nonetheless, [PERSON] et al. measured mobilities for CVD graphene rivaling those reported for similar devices based on exfoliated graphene [39]. This suggests that CVD samples are comparable in quality to large-area exfoliated single-crystals that contain intragranular line defects and other structural imperfections [40]. In this context, an atomic-scale analysis of the GBs detrimental effects on the transport properties of PG is required, with so far only a few first-principles studies characterizing charge transport through GBs. Importantly, [PERSON] et al. [41] showed that GBs degrading role could be alleviated through atomically precise manufacturing. A transport gap was also demonstrated to appear for specific types of GBs. However, experimentally-observed GBs exhibit more complicated arrangements of non-hexagonal rings [42] than atomic structures of ref. [41]. This necessarily leads to discrepancies between experimental measurements in PG and theoretical predictions of transport properties of \"ideal\" GBs. Our researches focus on the systematic study of the electronic transport through realistic graphene grain boundaries [43; 44] and on the exploration of novel phenomena such as valley-dependent transport, electron optics effects, Aharonov-Bohm interferences and spin-diffusion lengths in polycrystalline graphene [45; 46; 47]. Graphene GBs atomic structures were obtained using classical molecular dynamics with optimized Tersoff potentials [48]. This empirical potential model has been shown to accurately describe the structural properties of defective graphene [49]. The electronic properties of defective graphene systems under study were calculated using either the first-principles approach [44] or the \(\pi\)-orbital TB technique [43; 45; 46]. First-principles calculations were performed using DFT within the OpenMX code [50; 51; 52], a software package based on norm-conserving pseudo-potentials and pseudo-atomic localized basis functions. Parametrized TB models are very effective to model the electronic properties of graphene at low energies, i.e., around the Fermi level. The good agreement between these two approaches was demonstrated in refs. [41; 45]. Charge transport through GBs was simulated using the Landauer-Buttiker formalism implemented within the [PERSON]'s function approach.