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

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.

Figures (4)

• Figure 1: $|$Comparison of the electronic bands obtained from DFT and spectral function from DMFT. Momentum-resolved spectral function $A_{\mathbf{k}}(\varepsilon)$ of CeH$_9$ along a high-symmetry path calculated with DMFT (color map) compared to the energy bands calculated by DFT (solid red lines).
• Figure 2: $|$Comparison of density of states (DOS) per unit cell obtained from DFT and DMFT. a Electronic and b phononic DOS of CeH$_9$ calculated with DFT and DFT+DMFT, respectively. The inset in a highlights the increase in the DOS near the Fermi level.
• Figure 3: $|$Phonon and electron-phonon properties obtained from DFT and DMFT. Phonon dispersion, Eliashberg spectral function $\alpha^2F(\omega)$, and integrated electron-phonon coupling strength $\lambda(\omega)$ as a function of phonon frequency $\omega$ as calculated with a DFT and b DFT+DMFT. The linewidth of the phonon dispersion is proportional to $\lambda(\omega)$ projected onto the phonon modes.
• Figure 4: $|$Anisotropic superconducting gap of CeH$_9$. Calculated superconducting gap $\Delta$ on the Fermi surface at 10 K computed with a DFT and b DFT+DMFT. c Anisotropic Migdal-Eliashberg superconducting gap $\Delta$ as a function of temperature. We consider four cases: (top left) DFT electrons with DFT phonons, (bottom left) DMFT electrons with DFT phonons, (top right) DFT electrons with DMFT phonons, and (bottom right) DMFT electrons with DMFT phonons. The solid red line represents the temperature dependence of the superconducting gap expected from the BCS theory Bardeen1957 in the weak-coupling limit where $\Delta(T) = A \sqrt{1-T/T_\mathrm{c}}$, where $A$ is a fitting constant.