Two-particle scattering in graphene is a multichannel problem, where the energies of the identical or opposite-helicity channels lie in disjoint energy segments. Due to the absence of Galilean invariance, these segments depend on the total momentum $Q$. The dispersion relations for the two opposite-helicity scattering channels are analogous to those of two one-dimensional tight-binding lattices with opposite dispersion relations, which are known to easily bind states at their edges. When an $s$-wave separable interaction potential is assumed, those bound states reveal themselves as three Feshbach resonances in the identical-helicity channel. In the limit $Q\to 0$, one of the resonances survives and the opposite-helicity scattering amplitudes vanish.

• Received 17 July 2013
• Revised 10 December 2013

DOI:https://doi.org/10.1103/PhysRevB.89.045420