Superconductivity in Dopedsp3Semiconductors: The Case of the Clathrates

Abstract

We present a joint experimental and theoretical study of the superconductivity in doped silicon clathrates. The critical temperature in ${\mathrm{B}\mathrm{a}}_8@\mathrm{S}\mathrm{i}\mathrm{\text{−}}46$ is shown to strongly decrease with applied pressure. These results are corroborated by ab initio calculations using MacMillan’s formulation of the BCS theory with the electron-phonon coupling constant $\lambda$ calculated from perturbative density functional theory. Further, the study of ${\mathrm{I}}_8@\mathrm{S}\mathrm{i}\mathrm{\text{−}}46$ and of gedanken pure silicon diamond and clathrate phases doped within a rigid-band approach show that the superconductivity is an intrinsic property of the $s{p}^3$ silicon network. As a consequence, carbon clathrates are predicted to yield large critical temperatures with an effective electron-phonon interaction much larger than in ${\mathrm{C}}_{60}$.