Chiral gap and collective excitations in monolayer graphene from strong coupling expansion of lattice gauge theory

Using the strong coupling expansion of the compact and noncompact U(1) lattice gauge theories for monolayer graphene, we show analytically that fermion band gap and pseudo-Nambu-Goldstone exciton (π exciton) are dynamically generated due to chiral symmetry breaking. The mechanism is similar to the generation of quark mass and pion excitation in quantum chromodynamics (QCD). We derive a formula for the π-exciton analogous to the Gell-Mann-Oakes-Renner (GOR) relation in QCD. Experimental confirmation of the GOR relation on a suspended monolayer graphene would be a clear evidence of chiral symmetry breaking.