Thermoelectromechanical effects in relaxed-shape graphene and band structures of graphene quantum dots

We investigate the in-plane oscillations of relaxed-shape graphene due to externally applied tensile edge stress along both the armchair and zigzag directions. We show that the total elastic energy density is enhanced with temperature for the case of applied tensile edge stress along the zigzag direction. Thermoelectromechanical effects are treated via pseudomorphic vector potentials to analyze the influence of these coupled effects on the band structures of bilayer-graphene quantum dots. We report that the level crossing between the ground and first-excited states in the localized edge states can be achieved with accessible values of temperature. In particular, the level-crossing point extends to higher temperatures with decreasing externally applied tensile edge stress along the armchair direction. This kind of level crossing is absent in the states formed at the center of the graphene sheet due to the presence of threefold symmetry.