Possible enhancement of the superconducting $T_c$ due to sharp Kohn-like soft phonon anomalies

TL;DR

This paper explores how sharp phonon anomalies, such as Kohn-like soft phonon modes, can significantly enhance the electron-phonon coupling and potentially increase the superconducting transition temperature, offering a pathway to high-temperature superconductivity.

Contribution

The study introduces a theoretical framework showing that sharp phonon softening can boost electron-phonon coupling and $T_c$, highlighting a new mechanism for high-temperature superconductivity.

Findings

Sharp phonon dips can increase electron-phonon coupling $mbda$

Enhanced $mbda$ can lead to higher $T_c$ under certain conditions

Soft phonon anomalies in momentum space may enable high-temperature superconductivity

Abstract

Phonon softening is a ubiquitous phenomenon in condensed matter systems which is often associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relation, either acoustic or optical (including the case of Kohn-type anomalies typically associated with CDW), can cause a manifold increase of the electron-phonon coupling constant $\lambda$. This, under certain conditions, which are consistent with the concept of optimal frequency introduced by Bergmann and Rainer, can produce a large increase of the superconducting transition temperature $T_c$. In summary, our results suggest the possibility of reaching high-temperature superconductivity by exploiting soft phonon anomalies restricted in momentum space.