We predict a new mechanism of surface plasmon amplification in graphene-insulator-graphene van der Waals heterostructures. The amplification occurs upon the stimulated interlayer electron tunneling accompanied by the emission of a coherent plasmon. The quantum-mechanical calculations of the non-local high-frequency tunnel conductivity show that a relative smallness of the tunneling exponent can be compensated by a strong resonance due to the enhanced tunneling between electron states with

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... ear momenta in the neighboring graphene layers. With the optimal selection of the barrier layer, the surface plasmon gain due to the inelastic tunneling can compensate or even exceed the loss due to both Drude and interband absorption. The tunneling emission of the surface plasmons is robust against a slight twist of the graphene layers and might explain the electroluminescence from the tunnel-coupled graphene layers observed in the recent experiments.