Systematics in the superconducting and normal state properties in chemically substituted MgB$_{2}$

Abstract

The superconducting transition temperature, T$_{C}$, the residual resistivity $ρ_{0}$ and the slope of resistivity curve at high temperature, d$ρ$/dT, have been measured in a series of MgB$_{2}$ samples that have been chemically substituted to varying degree with Li or Cu at the Mg-site and by Li or Cu at the Mg-site along with C substitution at the B-site. DC resistivity and ac susceptibility measurements were employed to extract the above parameters. T$_{C}$ versus the electron count (estimated from simple chemical valence count arguments) shows a universal behaviour, with T$_{C}$ being constant at the MgB$_{2}$ value for electron counts lower than in MgB$_{2}$ but rapidly decreasing for larger electron counts. The temperature dependence of resistivity in the normal state fits to the Bloch- Gruneisen formula, from which the Debye temperature, $θ_{D}$, and the $ρ_{0}$ are extracted. $θ_{D}$ variation with T$_{C}$ is not systematic, whereas $ρ_{0}$ versus T$_{C}$ shows a systematic variation that depends on the type of the chemical substituent. This dependence has a signature of the nature of the intraband/interband scattering affected by the chemical substitutions. d$ρ$/dT increases with C substitution, but decreases with Li and Cu substitution, implying that C substitution leads to the domination of conductivity by the $σ$ band, while in the Li/Cu substituted samples the $π$ band dominates conduction.