The maximum Tc of conventional superconductors at ambient pressure

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow> <mml:mrow><mml:mi>log</mml:mi></mml:mrow> </mml:msub> </mml:math> rarely exceeds 1800 K. Our data reveals an inherent trade-off between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>ω</mml:mi></mml:mrow> <mml:mrow><mml:mi>log</mml:mi></mml:mrow> </mml:msub> </mml:math> 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 Li₂AgH₆ and its sibling Li₂AuH₆ 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.