Electron-phonon interactions and superconductivity in ${\mathrm{K}}_3$${\mathrm{C}}_{60}$

Using electronic states and phonon states from first-principles calculations on ${\mathrm{K}}_3$${\mathrm{C}}_{60}$ to evaluate the quantities in the McMillan equation, we examine the effects of both electron-phonon dynamic charge coupling (Q) and Jahn-Teller coupling (JT) on various superconducting properties, including ${\mathit{T}}_{\mathit{c}}$, Δ${\mathit{T}}_{\mathit{c}}$ (the shift of ${\mathit{T}}_{\mathit{c}}$ for 1 GPa pressure), ${\mathrm{\alpha }}_{\mathrm{C}}$ (the isotope exponent for ${}_{}{}^{12}{}_{}{}^{}\to _{}^{13}{}_{}{}^{}$C), and ${\mathrm{\alpha }}_{\mathrm{K}}$ (the isotope exponent for ${}_{}{}^{39}{}_{}{}^{}\to _{}^{41}{}_{}{}^{}$K). All quantities including electron-phonon coupling are evaluated (without modification) directly from theory, except for the screening length between conducting electrons and ions, ${\mathit{R}}_{\mathrm{sc}}$. With ${\mathit{R}}_{\mathrm{sc}}$=0.8–1.0 Å, we find that the calculated properties, ${\mathit{T}}_{\mathit{c}}$, Δ${\mathit{T}}_{\mathit{c}}$, and ${\mathrm{\alpha }}_{\mathrm{C}}$, are all in good agreement with experimental measurements. We find that the superconducting properties depend critically upon the synergy between Q and JT coupling.