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 $B-B$ 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.

• Received 27 February 2001

DOI:https://doi.org/10.1103/PhysRevB.64.144523