Electron-phonon or hole superconductivity in MgB2

Abstract

The BCS electron-phonon mechanism and the unconventional ``hole mechanism'' have been proposed as explanations for the high-temperature superconductivity observed in ${\mathrm{MgB}}_{2}.$ It is proposed that a critical test of which theory is correct is the dependence of ${T}_{c}$ on hole doping: the hole mechanism predicts that ${T}_{c}$ will drop rapidly to zero as holes are added, while the electron-phonon mechanism appears to predict increasing ${T}_{c}$ for a substantial range of hole doping. Furthermore, the hole mechanism and electron-phonon mechanism differ qualitatively in their predictions of the effect on ${T}_{c}$ of change in the $B\ensuremath{-}B$ distances. We discuss predictions of the hole mechanism for a variety of observables as a function of doping, emphasizing the expected differences and similarities with the electron-phonon explanation. The hole mechanism predicts coherence length and penetration depth to increase and decrease monotonically with hole doping, respectively.