Impact of Strain in Monolayer Graphene and Related Phenomena

It is well established, both theoretically and experimentally, that unstrained monolayer graphene shows linear dispersion as defined by Dirac equation of massless Fermions. But, when it is subjected to anisotropic strain, the two Dirac points get shifted from their equilibrium positions and they merge when the applied strain attains a threshold value. Near the merging point, dispersion energy is found to deviate from linearity and band gap opens up turning graphene to behave as semiconductor. A detailed calculation shows that unlike normal semiconductors with direct band gap its dispersion energy is non-parabolic around the merging point and the curvature of non-parabolicity changes with the variation of the direction of the applied anisotropic strain. Not only that, the threshold value of strain for band gap opening varies periodically between specified maximum and minimum as the strain is applied in the directions further away from the zigzag edge. To study these atypical features, a generalized expression for strain induced non-linear dispersion relation of monolayer intrinsic graphene has been formulated under tight-binding approximation (TBA). Also, the band gap energy, density of states (DOS) and electron effective mass (EEM) have been determined as a function of the magnitude of strain as well as its direction of application.