## 1 Introduction  
Graphene--a single layer of carbon atoms arranged in a honeycomb pattern--is the basic material for the family of low-dimensional allotropes of carbon known as carbon nanomaterials, such as carbon nanotubes and fullerenes, which exhibit unusual physical properties [1]. The high electron mobility, among other characteristics, makes graphene a subject of great interest in contemporary physics [2; 3; 4; 5]. The fact that graphene is a zero-gap semiconductor may be a disadvantage for some applications. A solution is to chemically doped the structure so as to shift the Fermi level or to open a sizable gap, or both [6]. In particular, simple substitutional doping with B [7], N [8], and other elements can be realized by a variety of methods, either during the growth or after the graphene synthesis [9]. In this respect, low-energy implantation of the ionized dopant atoms is a promising technique [10]. Nitrogen is an important element for producing n-doped nanocarbons. For that reason, doping carbon-based nanostructures with N has been investigated since a long time [11]. In recent years, different techniques have been developed to incorporate nitrogen in graphene at concentration of a few atomic percent [12; 13; 14]. Along with substitutional nitrogen impurities, pyridinic and pyrrol defects are created in variable proportions. In heavily-doped graphene compounds, the latter defects confer new and remarkable properties [14] to the samples and play an important role on their transport properties [12]. In particular, field-effect transistors with strong n-type characteristics, which remain stable in air for a long period, have been realized from post-synthesis N-doped graphene samples [13]. It is of course important to understand the effects of chemical doping on the electronic structure of graphene and on its quantum transport properties [15]. The electronic properties of graphene doped with nitrogen atoms have been analyzed by several groups [16; 17; 18; 19; 20; 21; 22; 23]. Substitutional N dopants shift the Fermi level above the Dirac energy, modify the electronic density of states and open a small band gap [16; 17; 19]. Also, theory predicts that charge transport in graphene becomes diffusive in the presence of N or B impurities at a concentration above \(\sim\)0.5 at.% [24]. All these effects affect the conductivity of the samples in a non-trivial way. There are more carriers available for transport in these systems than in pure graphene but, on the other hand, scattering by the dopant atoms reduces the electron relaxation time [23] and, hence, the mobility. Numerical calculations of charge transport in boron- and nitrogen-doped graphene sheets obtained by the Kubo-Greenwood formalism have been reported in Refs. [20; 24; 25; 26; 27]. These works are among the few available theoretical studies of quantum transport in doped graphene, if one excludes the case of carbon nanotubes [28; 29; 30; 31; 32] and finite-width graphene nanoribbons [33; 34; 35; 36; 37], which can be treated with the Landauer-Buttiker formalism [38]. All the theoretical works referred to above were performed in the framework of the Schrodinger equation. The two-dimensional Weyl-Dirac equation (Dirac equation for massless fermions) is a continuous-medium approximation of the Schrodinger equation of graphene that is valid at low energies, up to 1-2 eV excitations [39; 40]. In this framework, the dynamics of wave packets has been investigated recently in an ideal monolayer graphene [41; 42] and, subsequently, in a random potential landscape that models charge puddles [43; 44]. The scattering of Schrodinger and Weyl fermions by potential and magnetic barriers has also been the subject of recent studies [45; 46]. For solving the time-dependent Schrodinger and Weyl-Dirac equations, a numerical method based on the split-operator technique has been used [47; 48].