The Maximum $T_c$ of Conventional Superconductors at Ambient Pressure

Abstract

The theoretical maximum critical temperature ($T_c$) for conventional superconductors at ambient pressure remains a fundamental question in condensed matter physics. Through analysis of electron-phonon calculations for over 20,000 metals, we critically examine this question. We find that while hydride metals can exhibit maximum phonon frequencies of more than 5000 K, the crucial logarithmic average frequency $ω_\text{log}$ rarely exceeds 1800 K. Our data reveals an inherent trade-off between $ω_\text{log}$ and the electron-phonon coupling constant $λ$, suggesting that the optimal Eliashberg function that maximizes $T_c$ is unphysical. Based on our calculations, we identify Li$_2$AgH$_6$ and its sibling Li$_2$AuH$_6$ as theoretical materials that likely approach the practical limit for conventional superconductivity at ambient pressure. Analysis of thermodynamic stability indicates that compounds with higher predicted $T_c$ values are increasingly unstable, making their synthesis challenging. While fundamental physical laws do not strictly limit $T_c$ to low-temperatures, our analysis suggests that achieving room-temperature conventional superconductivity at ambient pressure is extremely unlikely.

Figures (13)

• Figure 1: Histogram of (top) the maxima ($\omega_\text{max}$) and logarithmic average ($\omega_\text{log}$) of phonon frequencies and (bottom) the electron-phonon coupling constants ($\lambda$) calculated for around 20 000 metals (see Refs. cerqueira2024searching).
• Figure 2: Scatter plot of $\omega_\text{log}$ versus $\lambda$ for all calculated systems, the contour lines are $T_\textrm{c}$ from McMillan's formula with $\mu^*=0.1$.
• Figure 3: Harmonic phonon band structure, density of phonon states, and Eliashberg spectral function $\alpha^2F(\omega)$ of Li2AgH6 calculated within the harmonic approximation.
• Figure 4: Scatter plot of the distance to the convex hull of stability versus the superconducting transition temperature for all compounds in our dataset. In orange we also indicate the Pareto front corresponding to this data. Compounds on the Pareto front are labeled.
• Figure :