Impact of electronic correlations on the superconductivity of high-pressure CeH$_9$

TL;DR

This study demonstrates that electronic correlations significantly enhance the superconducting critical temperature of CeH$_9$ under high pressure, aligning theoretical predictions with experimental results by combining advanced computational methods.

Contribution

It introduces a combined density functional theory and dynamical mean-field theory approach to accurately model electronic correlations in rare-earth superhydrides.

Findings

Electronic correlations increase the density of states at the Fermi level.

Correlations lead to a larger superconducting gap.

Superconducting critical temperature is doubled from 47 K to 96 K.

Abstract

Rare-earth superhydrides have attracted considerable attention because of their high critical superconducting temperature under extreme pressures. They are known to have localized valence electrons, implying strong electronic correlations. However, such many-body effects are rarely included in first-principles studies of rare-earth superhydrides because of the complexity of their high-pressure phases. In this work, we use a combined density functional theory and dynamical mean-field theory approach to study both electrons and phonons in the prototypical rare-earth superhydride CeH$_9$, shedding light on the impact of electronic correlations on its critical temperature for phonon-mediated superconductivity. Our findings indicate that electronic correlations result in a larger electronic density at the Fermi level, a bigger superconducting gap, and softer vibrational modes associated with hydrogen atoms. Together, the inclusion of these correlation signatures increases the Migdal-Eliashberg superconducting critical temperature from 47 K to 96 K, close to the measured 95 K. Our results reconcile experimental observations and theoretical predictions for CeH$_9$ and herald a path towards the quantitative modeling of phonon-mediated superconductivity for interacting electron systems.