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Among the family of currently known promising quasi-two-dimensional (2D) materials, the authors of this survey concentrate on the problem of functionalization of the graphene- and phosphorene-based structures. In most cases, the modification of their properties occurs through the covalent or noncovalent surface functionalization and mechanical affects. The atomic structures and some physicochemical features of 2D materials possessing novel properties as compared to their bulk counterparts are analysed. Their main advantages are the thickness of one or more atoms, the absence of surface-broken bonds, high mobility of charge carriers, the flexibility, the ability to be combined artificially into coplanar (lateral) or lamellar heterostructures, as well as the possibility to manipulate widely the band-gap changing from the semi-conducting state even into the semi-metallic one (or vice versa) when needed. In order to reveal new factors affecting the electronic properties of 2D materials by means of the computational experiment using the author’s (self-constructed) software code, a series of studies are carried out. They are the calculations of the spatial distribution of valence electrons’ density, the electron densities of states, the band-gap widths, Coulomb potentials along selected directions, the charge values in regions of different-size material, the dielectric matrices, the macroscopic relative permittivities, and absorption spectra. A series of recent studies, which the authors carried out modelling the electronic and transport properties of single- or multilayer graphene films subjected to deformation or/and magnetic fields and containing different-type (point- or/and linear-acting) defects is reviewed. Analysing the obtained results and revealed effects, it is claimed that the uniaxial tensile deformations or shear deformations along with their combinations as well as the structural imperfections (mainly, the mutually configured defects) can be useful for achieving the new level of functionalization of graphene. So, for modification of its electrotransport properties through tuning the band-gap value as much as it is enough to achieve the graphene transformation from the zero-band-gap semi-metallic state into the semi-conducting state and even reach the gap values, which are substantially higher than that for some materials (including silicon) currently used widely in the nanoelectronic devices. The strain- and defect-induced electron–hole asymmetry and anisotropy of conductivity and its nonmonotony as a function of deformation suggest a confidence in manipulating the electrotransport properties of graphene-like and beyond quasi-2D materials through a variety of both strains and defects. The use of reviewed and analysed results serves as a significant step in improving the properties of the considered materials in order to implement the multifunctional applications of them in the immediate prospect.

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