Plasmons in tunnel-coupled graphene layers: Backward waves with quantum cascade gain

We theoretically demonstrate that graphene-insulator-graphene tunnel structures can serve as plasmonic gain media due to the possibility of stimulated electron tunneling accompanied by emission of plasmons under application of interlayer voltage. The probability of plasmon-assisted tunneling is resonantly large at certain values of frequency and interlayer voltage corresponding to the transitions between chiral electron states with collinear momenta, which is a feature unique to the linear bands of graphene. The plasmon dispersion develops an anticrossing with the resonances in tunnel conductivity and demonstrates negative group velocity in several frequency ranges.