COUPLED EFFECT OF STRAIN AND MAGNETIC FIELD ON ELECTRONIC BAND STRUCTURE OF GRAPHENE

Hofstadter's fractal energy spectrum, which is also called Hofstadter butterfly, remained as one of the most interesting topics of condensed matter physics for decades. We study, in this paper, how different patterns of energy spectrum emerge when a graphene sheet is subjected to in-plane uniaxial and shear strain in the presence of transverse magnetic field. We discuss these patterns in the context of opening of the electronic energy band structure of graphene. We thus provide a uni fied framework for graphene under the coupled e r ect of strain and magnetic field. Due to such coupling, the energy bandgap opens when certain threshold of strain in the zigzag direction of graphene is crossed. The threshold strain value depends on the rationality of the parameter phi/phi(0), i. e., the ratio of magnetic degrees ux through the deformed hexagonal plaquette and the quantum degrees ux (h/e). Numerical results shows that the energy bandgap depends nonlinearly on the magnitude of strain, and that the threshold strain and energy gap decrease with decreasing magnetic field.