Pairing amplification induced by nonadiabatic effects on the electron-phonon interaction throughout the BCS-BEC crossover

TL;DR

This study investigates how nonadiabatic effects influence electron-phonon interactions across the BCS-BEC crossover, revealing conditions that amplify pairing and are relevant for unconventional superconductors.

Contribution

It provides a detailed analysis of nonadiabatic corrections in a 2D system during the BCS-BEC crossover, highlighting their role in pairing amplification.

Findings

Nonadiabatic effects enhance pairing in the crossover regime.

Amplification is strongest at phonon energies comparable to hopping energy.

Relevant for understanding unconventional superconductor behavior.

Abstract

Nonadiabatic effects in the electron-phonon coupling are important whenever the ratio between the phononic and the electronic energy scales, the adiabatic ratio, is non negligible. For superconducting systems, this gives rise to additional diagrams in the superconducting self-energy, the vertex and cross corrections. In this work we explore these corrections in a two-dimensional single-band system through the crossover between the weak-coupling BCS and strong-coupling Bose-Einstein regimes. By focusing on the pseudogap phase, we identify the parameter range in which the pairing amplitude is amplified by nonadiabatic effects and map them throughout the BCS-BEC crossover. These effects become stronger as the system is driven deeply in the crossover regime, for phonon frequencies of the order of the hopping energy and for large enough electron-phonon coupling. Finally, we provide the phase space regions in which the effects of nonadiabaticity are more relevant for unconventional superconductors.