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.

Figure 1

(Color online) Top: Direct lattice and unit cell for monolayer graphene. Bottom: First Brillouin zone and Fermi points. The vectors ${\vec{K}}_1^{\prime },{\vec{K}}_1^{″}$ $({\vec{K}}_2^{\prime },{\vec{K}}_2^{″})$ are equivalent to ${\vec{K}}_1$ $\left({\vec{K}}_2\right)$.