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An analytical study of low-energy electronic excited states in an uniformlystrained graphene is carried out up to second-order in the strain tensor. Wereport an new effective Dirac Hamiltonian with an anisotropic Fermi velocitytensor, which reveals the graphene trigonal symmetry being absent in low-energytheories to first-order in the strain tensor. In particular, we demonstrate thedependence of the Dirac-cone elliptical deformation on the stretching directionrespect to graphene lattice orientation. We further analytically calculate theoptical conductivity tensor of strained graphene and its transmittance for alinearly polarized light with normal incidence. Finally, the obtainedanalytical expression of the Dirac point shift allows a better determinationand understanding of pseudomagnetic fields induced by nonuniform strains.

Low-energy theory for strained graphene: an approach up to second-order in the strain tensor