Electromagnetic properties of a double-layer graphene system with electron-hole pairing

We study electromagnetic properties of a double-layer graphene system in which electrons from one layer are coupled with holes from the other layer. The gauge invariant linear response functions are obtained. The frequency dependences of the transmission, reflection, and absorption coefficients are computed. We predict a peak in the reflection and absorption at the frequency equal to the gap in the quasiparticle spectrum. It is shown that the electron-hole pairing results in an essential modification of the spectrum of surface TM plasmons. We find that the optical TM mode splits into a low frequency undamped branch and a high frequency damped branch. At zero temperature the lower branch disappears. It is established that the pairing does not influence the acoustic TM mode. It is also shown that the pairing opens the frequency window in the subgap range for the surface TE wave.