Generalizing the Fermi velocity of strained graphene from uniform to nonuniform strain

•The relevance of the strain-induced Dirac point shift to obtain the anisotropic Fermi velocity is shown.•An appropriate expression of the position-dependent Fermi velocity is reported.•A position-dependent Fermi velocity induces an inhomogeneity in the carrier probability density.

The relevance of the strain-induced Dirac point shift to obtain the appropriate anisotropic Fermi velocity of strained graphene is demonstrated. Then a critical revision of the available effective Dirac Hamiltonians is made by studying in detail the limiting case of a uniform strain. An effective Dirac Hamiltonian for nonuniform strain is thus reported, which takes into account all strain-induced effects: changes in the nearest-neighbor hopping parameters, the reciprocal lattice deformation and the true shift of the Dirac point. Pseudomagnetic fields are thus explained by means of position-dependent Dirac cones, whereas complex gauge fields appear as a consequence of a position-dependent Fermi velocity. Also, position-dependent Fermi velocity effects on the spinor wavefunction are considered for interesting cases of deformations such as flexural modes.