$^{10}$B–$^{11}$B isotope substitution and superconductivity in ZrB$_{12}$

The specific heat of the ZrB$_{12}$ compound in the normal and superconducting states ($T_C\approx6$ K) has been studied in the $1.9$–$7$ K temperature range for high-quality single crystals with different relative contents of boron isotopes. For Zr$^{10}$B$_{12}$, Zr$^{\rm nat}$B$_{12}$, and Zr$^{11}$B$_{12}$ dodecaborides, the electron density of states and the electronphonon coupling constant, $\lambda _{\rm e{-}ph}\sim0.4$, are found. The dependence of the thermodynamic and upper critical fields, as well as of the Ginzburg-Landau parameter ($\kappa =0.8$–$1.14$) on temperature and isotope composition is determined. The results suggest the existence of the magnetic field induced phase transition at $T^*=4$–$5$ K, which is not related to the transition from type-I to type-II superconductivity. The possibilities of the existence of two-gap superconductivity and a structural phase transition at $T^*$ in zirconium dodecaboride are discussed.