Bose–Einstein condensation of paired photon-dressed electrons in graphene

• We point out the possibility of BEC of paired photon-dressed electrons in graphene.
• Analytically we calculate the fraction of condensed photon-dressed electron pairs.
• The condensation presents a strong dependence on the electron–photon bound energy.
• The pairing grows with the field, presenting a crossover from BCS state to BEC.

In this paper we point out the possible observation of the Bose–Einstein condensation for a gas of paired photon-dressed electrons in a graphene monolayer. At T=0 the condensation presents a strong crossover from the BCS state to the Bose–Einstein condensate. In an explicit way we calculated the fraction of condensed photon-dressed electron pairs as a function of the photon–electron bound energy and the temperature. The range of coherence of condensed quasiparticles is circumscribed to local bound states, where the Off-diagonal long-range order is guaranteed via the BCS state.