Effective field theory for the quantum electrodynamics of a graphene wire

We study the low-energy quantum electrodynamics of electrons and holes in a thin graphene wire. We develop an effective field theory (EFT) based on an expansion in p/ pT, where pT is the typical momentum of electrons and holes in the transverse direction, while p are the momenta in the longitudinal direction. We show that, to the lowest order in (p/ pT), our EFT theory is formally equivalent to the exactly solvable Schwinger model. By exploiting such an analogy, we find that the ground state of the quantum wire contains a condensate of electron-hole pairs. The excitation spectrum is saturated by electron-hole collective bound states, and we calculate the dispersion law of such modes. We also compute the dc conductivity per unit length at zero chemical potential and find gs e2 h, where gs =4 is the degeneracy factor.