Symmetry-based approach to electron-phonon interactions in graphene

We use the symmetries of monolayer graphene to write a set of constraints that must be satisfied by any electron-phonon interaction Hamiltonian. The explicit solution as a series expansion in the momenta gives the most general, model-independent couplings between electrons and long-wavelength acoustic and optical phonons. As an application, the possibility of describing elastic strains in terms of effective electromagnetic fields is considered in detail, with an emphasis on group-theory conditions and the role of time-reversal symmetry.