Electron-Phonon or Hole Superconductivity in $MgB_2$?

Abstract

The BCS electron-phonon mechanism and the unconventional 'hole mechanism' have been proposed as explanations for the high temperature superconductivity observed in $MgB_2$. It is proposed that a critical test of which theory is correct is the range of hole doping over which $T_c$ will be high: the hole mechanism predicts that $T_c$ will drop to zero for approximately 0.12 added holes per $B$ atom, while the electron-phonon mechanism appears to predict increasing $T_c$ for up to 0.36 holes added per $B$ atom. Furthermore, the hole mechanism and electron-phonon mechanism differ qualitatively in their predictions of the effect on $T_c$ of change in the $B-B$ 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.