# Computational Atomistic Modeling in Carbon Flatland and Other 2D Nanomaterials
## 2 Electronic Transport in Polycrystalline Graphene
This implies that the transport gap depends on the smallest perceptible periodicity while perturbations in periodicity induce leakage currents. In a nutshell, disorder is found to normalize the transport properties of PG (metallic or semi-conducting) [44]. On the one hand, the disordered nature of GBs increases scattering, reducing the overall transmissions in transparent systems, on the other hand, it induces leakage currents which damage the transport gap for reflective configurations. Owing to the misorientation between grains, the transport through GBs has been also shown to be highly sensitive to the effect of strains [43]. This is essentially due to the fact that even though the metallicity of graphene is still conserved, its Brillouin zone is strongly deformed and Dirac cones can be displaced in the momentum space when strains are applied. Moreover, such displacements of the Dirac cones are strongly dependent of the crystallographic orientation of graphene with respect to the strain direction. On this basis, the strain effects in PG can result in different momentum displacements of Dirac cones in two graphene grains surrounding a given GB, thus strongly modifying the low-energy transport properties through the system. In particular, while the transport gap in the boundary of class-II is modifiable, a uniaxial strain applied in proper directions can always open a gap in the boundary of class-I as illustrated in Figure 2. Interestingly, a large gap of a few hundred meV can be achieved with a small strain of a few percents only. The value of this gap has been shown to depend on three main parameters: the uniaxial strain magnitude, the uniaxial strain direction, and the lattice symmetry of graphene grains [43]. Figure 1: Electronic transport through graphene grain boundaries (GBs). Atomic structures of (**a**) the \((2,1)|(2,1)\) class-I GB, (**b**) the \((5,0)|(3,3)\) class-II GB, (**e**) the \((11,3)|(10,5)\) class-I GB and (**f**) the \((24,0)|(16,12)\) class-II GB. The zero-bias conductances are given in (**c**,**d**) for class-I and class-II systems, respectively. Conductances through the smallest (blue lines) and largest (orange lines) GBs are compared to pristine graphene (black dashed lines). Reprinted and adapted with permission from reference [44]. In addition to its dependence on the GBs and crystallographic orientation of grains, the transport through PG also represents interesting magnetotransport phenomena. For instance, it has been shown in ref. [53] that the formation of Landau levels is limited by the grain size and cannot be observed until the magnetic length is smaller than the average grain radius. The electron localization is also found to be unusual. In particular, strongly localized states and extended electronic states are at the center and between Landau levels, respectively. These extended states are developed along the network of GBs, explaining a finite value for the bulk dissipative conductivity and suppression of the quantized Hall conductance. A novel fascinating magnetotransport feature has been recently predicted in polycrystalline graphene [46]. In particular, the extended states strongly localized along the grain boundaries can be exploited to create tunneling paths connecting quantum Hall edge channels in CVD graphene samples. Consequently, strong Aharonov-Bohm (AB) interferences in the quantum Hall regime can be achieved in the PG systems schematized in Figure 3a. The AB oscillations in the conductance in a typical system are indeed illustrated in Figure 3b. These predicted AB oscillations are clarified by the pictures of the local density of left-injected electronic states in Figure 3c,d and can be essentially explained as follows. First, under a strong magnetic field, electrons in the internal graphene grain have to propagate following quantum Hall edge states. Second, because of defect scattering at the GBs, these electrons can circulate inside such graphene grain (i.e., along its edge).