The Maximum $T_c$ of Conventional Superconductors at Ambient Pressure

TL;DR

This study analyzes electron-phonon data for over 20,000 metals to estimate the maximum achievable critical temperature ($T_c$) for conventional superconductors at ambient pressure, concluding that room-temperature superconductivity is highly unlikely due to physical and stability constraints.

Contribution

It provides a comprehensive analysis of electron-phonon interactions across many metals to identify theoretical limits of $T_c$ and highlights the unphysical nature of the optimal Eliashberg function.

Findings

Hydride metals can have phonon frequencies over 5000 K.

The logarithmic average frequency $_ ext{log}$ rarely exceeds 1800 K.

Higher $T_c$ compounds tend to be thermodynamically unstable.

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 $\omega_\text{log}$ rarely exceeds 1800 K. Our data reveals an inherent trade-off between $\omega_\text{log}$ and the electron-phonon coupling constant $\lambda$, 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.