Anharmonicity and Coulomb pseudopotential effects on superconductivity in YH$_6$ and YH$_9$

TL;DR

The paper tackles the discrepancy between experimental and theoretical $T_c$ values for YH$_6$ and YH$_9$ by using the stochastic path-integral approach (SPIA) to capture quantum and anharmonic ion dynamics. SPIA computes the effective electron-electron interaction via fluctuating electron-ion scattering, yielding $\lambda(m)$ and $\bar{\nu}_2$, and leverages an isotropic Eliashberg framework with a renormalized $\mu^*$ to predict $T_c$. The results show that anharmonic corrections substantially modify EPC and phonon frequencies, and that incorporating the frequency-cutoff renormalization of $\mu^*$ produces Tc values in close agreement with experiments (roughly $T_c \approx 212$ K for YH$_6$ and $T_c \approx 240$ K for YH$_9$). This work demonstrates that anharmonicity, when paired with proper Coulomb renormalization, can explain the observed Tc and establishes SPIA as a versatile tool for predicting superconductivity in hydrogen-rich materials.

Abstract

Anharmonic effects are widely believed to be the primary cause of the overestimation of superconducting transition temperatures of yttrium hydrides YH$_6$ and YH$_9$ in theoretical predictions. However, prior studies indicate that anharmonicity alone may be insufficient to account for this discrepancy. In this work, we employ the stochastic path-integral approach to investigate the quantum and anharmonic effects of ions in yttrium hydrides. Our calculations reveal significant corrections to the electron-phonon coupling parameters and an increase in the average phonon frequency compared to density functional perturbation theory, aligning closely with results from the stochastic self-consistent harmonic approximation. We find that properly taking into account the renormalization of the Coulomb pseudopotential due to the frequency cutoff, which is often overlooked in previous calculations, is critical to predicting transition temperatures consistent with experimental values for both YH$_6$ and YH$_9$. This indicates that, with this correction, anharmonic effects are sufficient to explain the discrepancies between experimental and theoretical results.

Figures (5)

• Figure 1: Trajectories of centroid mode of all hydrogen (gray) and yttrium (blue) ions in PIMD simulation for (a) YH$_6$ under 165 GPa at 220 K from [100] view, and (c) YH$_9$ under 255 GPa at 240 K from [001] view. (b) and (d) are corresponding RDFs.
• Figure 2: (a) EPC parameters $\lambda(m)$ of YH$_6$ under 165 GPa at 220 K. DFPT and SSCHA results are calculated using the Eliashberg spectral functions presented in Ref. YH6_exp1. (b) EPC parameters $\lambda(m)$ of YH$_9$ under 255 GPa at 240 K. DFPT result is calculated using the Eliashberg spectral function presented in Ref. YH9_phase under 260 GPa. The inset shows the asymptotic behavior of $\bar{\nu}_2(m)=2\pi/\hbar\beta\sqrt{m^2\lambda(m)/\lambda(0)}$, whose asymptotic value gives the average phonon frequency $\bar{\nu}_2$.
• Figure 3: $T_c$ values of YH$_6$ and YH$_9$ at various pressures. Filled points indicate experimental data from Refs. YH6_exp1YH_exp2YH_exp3. Empty points represent theoretical predictions from Refs. YH6_exp1YH9_phase and our SPIA calculations. $\mu^* = 0.11$ is used in all calculations.
• Figure 4: The relation between $T_c$ and frequency cutoff when solving the linearized Eliashberg equation. The truncation $N$ denotes the frequency cutoff at $\omega_N=(2N+1)\pi/\hbar\beta$. The blue line is calculated with the bare $\mu^*=0.11$ while the red line is calculated with the renormalized $\mu^*(N)$ defined in Eq. \ref{['eq:mustar']}. The Eliashberg spectral function used in calculation is the SSCHA result of YH$_6$ from Ref. YH6_exp1.
• Figure 5: EPC parameters $\lambda(m)$ of (a) YH$_6$ and (b) YH$_9$ with respect to the $\boldsymbol{k}$-grid density of the supercell. The asymptotic behavior of $m^2\lambda(m)$ is shown in the inset.