Superconductivity in 2D Systems Enhanced by Nonadiabatic Phonon-Production Effects

We investigate the dynamical effects of electron-phonon coupling (EPC) on thesuperconducting properties of two-dimensional (2D) systems, calculating theEliashberg function in terms of dynamically renormalized phonons. By studyingdifferent approximations for the phonon self-energy, we identify the importantrole of charge fluctuations in shaping the superconductivity properties, notonly through the renormalization of phonon frequencies and damping rates butalso through structural changes in the phonon spectral function. With thedynamical effects treated consistently, we argue that a part of the phononspectral weight necessarily shifts to low frequencies due to the coupling tothe 2D gapless plasmon. Furthermore, we find that the EPC leads to excessphonon spectral weight as well - i.e., phonon production - which generallytends to enhance the transition temperature. Our calculations point out thatthe influence of phonon production becomes greater as the density and theeffective mass of electrons increase.