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Thermo-electromechanical effects in relaxed shape graphene and bandstructures of graphene quantum dots

We investigate the in-plane oscillations of the 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. Thermo-electromechanical effects are treated via pseudomorphic vector potentials to analyze the influence of these coupled effects on the bandstructures of bilayer graphene quantum dots (QDs). We report that the level crossing between ground and first excited states in the localized edge states can be achieved with the accessible values of temperature. In particular, the level crossing point extends to higher temperatures with decreasing values of externally applied tensile edge stress along the armchair direction. This kind of level crossings is absent in the states formed at the center of the graphene sheet due to the presence of three fold symmetry.