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Using first-principles density functional theory calculations, the mechanical and electronic properties of the three main (β12, χ3, and striped) phases of single-layer borophene sheets are calculated under in-plane uniaxial/biaxial strain, including the harmonic strain-energy regions of β12, χ3, and striped phases over the strain ranges of −3.5%–3.5%, −4.5%–4.5%, and −2.5%–2.5%, respectively, along the x direction (the direction of the highest bond orientation). We introduce a method by which the nonlinear behavior of these and any other two-dimensional materials can be investigated even above their ultimate strains, beyond which no-uniform plastic deformation occurs. Defining an appropriate deformation, and utilizing both continuum modeling and special equations based on the density functional theory, a method of computing second-, third-, and fourth-order elastic constants of the three different phases of borophene is presented that utilizes rectangular unit cells, which can substitute for any two-dimensional unit cell. Using this new method, 4 independent second-order, 6 third-order, and 9 fourth-order elastic constants are calculated, which is the complete set of elastic constants for two-dimensional structures. The electronic band structure of borophene shows anisotropic electronic behavior. Despite the metallic character of borophene sheets, applying directional strain based on deformation matrices creates a bandgap in some regions of the Brillouin zones, opening up the possibility of mechanical control of electronic properties.

Between the ferromagnetic semiconductors of the III‐V group, the transition metals (TMs) doped gallium nitride (Ga, TM)N diluted magnetic semiconductor (DMS) shows the most well‐understood and promising applications in spintronic, due to its high Curie temperature. In this research, electronic and magnetic properties of pure armchair (3, 3) and zigzag (5, 0) gallium nitride nanotubes (GaNNTs) and doped with TMs are investigated using the spin‐polarized density functional theory. The spin‐polarized DOS revealed that pure zigzag and armchair GaNNTs are nonmagnetic semiconductors with a direct and indirect bandgap, respectively, in contrast, TMs doped GaNNTs are DMS or half metals (HM). Our results show a high Curie temperature of more than 823 K for Cr and Mn doping, indicating may be good room‐temperature ferromagnetic material for spintronic applications in the future. 11% Cr and Mn atoms doped (3, 3) GaNNT are HM with 100% spin polarization and appear to be good candidates for spintronic applications and especially as spin filter devices.

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