Band structure of stress-strain graphene

Ideal graphene exhibits conductive properties due to the absence of a band gap in its electron spectrum. A number of experimental studies demonstrate the possibility of obtaining a band gap in graphene by placing it on various substrates. Graphene on a substrate can undergo various types of structural deformations, which affects the electronic structure of the material under study. In this paper, an approach is proposed for accounting for the influence of elastic and plastic deformation fields on the electronic structure of graphene-like structures within the framework of the tight-binding model. The novelty of the proposed model lies in its consideration of the inhomogeneity of the hopping integral between nearest-neighbor atoms. A method is presented for estimating the main energy parameter of the model—the matrix element of the transition between nearest carbon atoms (hopping integral)—in the region of local deformation of the graphene structure caused by a loop dislocation. The dependence of the electron energy spectrum on the magnitude of the uniaxial and shear components of the strain tensor is proposed and analyzed. Analysis of the model revealed the effect of movement and merging of Dirac cones. The study demonstrates that only after fusion does the band gap open and further expand under shear deformation. With only diagonal components of the strain tensor, fusion of Dirac points does not occur, and no band gap appears. Based on the constructed model, it is possible to predict the required strain values ??to achieve a stable band gap in graphene, and therefore its semiconductor properties. The resulting model also demonstrates the possibility of controlling the semiconductor properties.