Superconducting properties of the atomically disordered MgB$_2$ compound

The effect of disorder induced by neutron irradiation in a nuclear reactor (thermal neutron fluence $1\times10^{19}\,$cm$^{-2}$) on the superconducting transition temperature $T_c$ and the upper critical field $H_{c^2}$ of polycrystalline MgB$_2$ samples was investigated. Despite the appreciable radiation-induced distortions (more than ten displacements per atom), the initial crystal structure (C32) was retained. The temperature $T_c$ decreased from $38$ to $5$ K upon irradiation and was practically completely restored after the subsequent annealing at a temperature of $700^\circ$C. A weak change in the $dH_{c^2}/dT$ derivative upon irradiation is explained by the fact that the irradiated samples are described by the «pure» limit of the theory of disordered superconductors. The suppression of $T_c$ upon disordering may be due to the isotropization of the originally anisotropic (or multicomponent) superconducting gap or to a decrease in the density of electronic states at the Fermi level.