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Analytical calculation of electron's group velocity surfaces in uniform strained graphene

Electron group velocity for graphene under uniform strain is obtained analitically by using the Tight-Binding approx- imation. Such closed analytical expressions are useful in order to calculate electronic, thermal and optical properties of strained graphene. These results allow to understand the behavior of electrons when graphene is subjected to strong strain and nonlinear corrections, for which the usual Dirac approach is not longer valid. Some particular cases of uni- axial and shear strain were analized. The evolution of the electron group velocity indicates a break up of the trigonal warping symmetry, which is replaced by a warping consistent with the symmetry of the strained reciprocal lattice. The Fermi velocity becomes strongly anisotropic, i.e, for a strong pure shear-strain (20% of the lattice parameter), the two inequivalent Dirac cones merge and the Fermi velocity is zero in one of the principal axis of deformation. We found that non-linear terms are essential to describe the effects of deformation for electrons near or at the Fermi energy.