Giant Eliashberg enhancement of superconductivity in flat bands*

The enhancement of superconductivity under appropriate electromagnetic radiation due to redistribution of quasiparticles into a more favorable nonequilibrium configuration is called Eliashberg effect. Here, we investigate the Eliashberg effect in flat band superconductors. While the superconductivity in flat bands is established by non-trivial winding of wavefunction of the slow-moving electrons, the Eliashberg enhancement is completely determined by the density of states which for flat bands is peaked in a narrow range of energies. We show that this large density of states in flat band materials can mediate a drastic enhancement of superconductivity when the material is irradiated with a light of frequency under pair breaking limit and band width. Assuming BCS coupling, we illustrate this enhancement in flat bands of twisted bilayer graphene. This opens new possibilities of nonequilibrium phenomena driven by peaked density of states in flat band superconductors, e.g., superfluid density and supercurrent.