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 non-compact U(1) lattice gauge theory for monolayer graphene, we show analytically that fermion bandgap and pseudo Nambu--Goldstone exciton (pi-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 pi-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.