Screening Induced Crossover between Phonon- and Plasmon-Mediated Pairing in Layered Superconductors

Two-dimensional (2D) metals can host gapless plasmonic excitations, which strongly couple to electrons and thus may significantly affect superconductivity in layered materials. To investigate the dynamical interplay of the electron-electron and electron-phonon interactions in the theory of 2D superconductivity, we apply a full momentum- and frequency-dependent one-loop theory treating electron-phonon, electron-plasmon, and phonon-plasmon coupling with the same accuracy. We tune the strength of the Coulomb interaction by varying the external screening $\varepsilon_{ext}$ to the layered superconductor and find three distinct regions. At weak screening, superconductivity is mediated by plasmons. In the opposite limit conventional electron-phonon interactions dominate. In between, we find a suppressed superconducting state. Our results show that even conventional electron-phonon mediated layered superconductors can be significantly affected by the electron-plasmon coupling in a weak screening environment. This unconventional pairing contribution can then be controlled by the external screening.