Influence of Coulomb interactions on Einstein phonons in a three-dimensional electron gas and superconductivity

Abstract

This study investigates the influence of Coulomb interactions on Einstein phonons in a three-dimensional electron gas (3DEG) and their impact on superconducting properties. By considering Coulomb effects in all contributions to the phonon self-energies, we explore the renormalization of phonons and its implications for superconductivity. Numerical solutions of the isotropic Eliashberg equations are used to determine the gap functions, providing valuable insights into the behavior of renormalized phonons. Our analysis reveals that while the frequencies of renormalized phonons are lower compared to non-interacting Einstein phonons, their inclusion leads to higher superconducting critical temperatures and maximum gap functions. However, as the strength of Coulomb interactions increases, a decrease in the superconducting critical temperature and gap is observed. These findings highlight the significant role of Coulomb interactions in determining the behavior of phonons and the emergence of superconductivity in three-dimensional electron gases.