The discrepancies in the literature regarding the fingerprints of different types of deformation in the electronic structure of even perfect graphene without any structural defects and external magnetic fields are review in Ref. . Here, we present results of numerical study on a role of tensile and shear strains and external magnetic field in their impact on electronic density of states (DOS) of graphene when it is perfect (defect-free) and imperfect (contains defects). The DOS is calculated using the tight-binding Hamiltonian, where the perpendicular magnetic field, uniaxial tension and shear strain are included via relevant modifications of hopping parameters. If the graphene sample is a defect-free, the combination of shear and uniaxial zigzag strains is found to be much more efficient source for the band-gap opening and tuning than they are applied separately. Observed non-equidistant Landau levels (LLs) in the energy spectrum of a defectless graphene undergo the displacement towards the non-shiftable zero-energy Landau level (LL), thus they get contraction as the uniaxial tension is applied independently on the stretching direction. The presence of both point and extended defects reduces LLs peaks, broadens, smears, and can even suppress the LLs depending on a degree of disorders, their strength, and largely effective ranges. Splitting of the zero-energy LL is observable in case of a short-range disorder. Alteration of the localized electronic states in graphene is sensitive to the axis of strain: the uniaxial tensile strains along armchair- and zigzag-edge directions can result to competing phenomena associated with enhancement and reduction of the DOS, respectively. Mutual action of perpendicular magnetic field and uniaxial stress along the zigzag direction in graphene contributes to the band gap in its energy spectrum: the gap becomes more pronounced and even wider than it is in case of a zigzag strain effect only.
Sagalianov I.Yu., Radchenko T.M., Prylutskyy Yu.I., Tatarenko V.A., Szroeder P. Mutual influence of uniaxial tensile strain and point defect pattern on electronic states in graphene // Eur. Phys. J. B. – 2017. – 90. – P. 112.