Within the tight binding approximation, we study the dependence of the electronic band structure and of the optical conductivity of a graphene single layer on the modulus and direction of applied uniaxial strain. While the Dirac cone approximation, albeit with a deformed cone, is robust for sufficiently small strain, band dispersion linearity breaks down along a given direction, corresponding to the development of anisotropic massive low-energy excitations. We recover a linear behavior of the low-energy density of states, as long as the cone approximation holds, while a band gap opens for sufficiently intense strain, for almost all, generic strain directions. This may be interpreted in terms of an electronic topological transition, corresponding to a change of topology of the Fermi line, and to the merging of two inequivalent Dirac points as a function of strain. We propose that these features may be observed in the frequency dependence of the longitudinal optical conductivity in the visible range, as a function of strain modulus and direction, as well as of field orientation.Comment: Phys. Rev. B, to appea

After deriving a general correspondence between linear response correlation functions in graphene with and without applied uniaxial strain, we study the dependence on the strain modulus and direction of selected electronic properties, such as the plasmon dispersion relation, the optical conductivity, as well as the magnetic and electric susceptibilities. Specifically, we find that the dispersion of the recently predicted transverse plasmon mode exhibits an anisotropic deviation from linearity, thus facilitating its experimental detection in strained graphene samples.Comment: Phys. Rev. B, to appea