Trigonal warping and photo-induced effects on zone boundary phonon in monolayer graphene

We have reported the electronic band structure of monolayer graphene when the combined effects arising from the trigonal warp and highest zone-boundary phonons having A1g symmetry with Haldane interaction which induced photo-irradiation effect. On the basis of our model, we have introduced a diagonalization to solve the associated Fröhlich Hamiltonian. We have examined that, a trigonal warping effect is introduced on the K and K' points, leading to a dynamical band gap in the graphene electronic band spectrum due to the electron-A1g phonon interaction and Haldane mass interaction. Additionally, the bands exhibited an anisotropy at this point. It is also found that, photo-irradiation effect is quite smaller than the trigonal warp effects in the graphene electronic band spectrum. In spite of this, controllability of the photo induced effects by the Haldane mass will have extensive implications in the graphene.