Two-gap superconductivity inZrB12: Temperature dependence of critical magnetic fields in single crystals

We report the measurements of the temperature dependence of the resistivity, $\rho \left(T\right)$, magnetic penetration depth, $\lambda \left(T\right)$, the lower, $H_{c1}\left(T\right)$, and upper, $H_{c2}\left(T\right)$, critical magnetic fields, for single crystals of dodecaboride $\mathrm{Zr}{\mathrm{B}}_{12}$, diboride $\mathrm{Zr}{\mathrm{B}}_2$, and thin films of diboride $\mathrm{Mg}{\mathrm{B}}_2$. We observe a number of deviations from conventional behavior in these materials. Although $\mathrm{Zr}{\mathrm{B}}_{12}$ behaves like a simple metal in the normal state, the resistive Debye temperature, $300\mathrm{K}$, is three times smaller relative to that $(800–1200\mathrm{K})$ calculated from the specific heat, $C\left(T\right)$, data. We observe predominantly quadratic temperature behavior of resistivity in $\mathrm{Zr}{\mathrm{B}}_{12}$ below $25\mathrm{K}$ and in $\mathrm{Zr}{\mathrm{B}}_2$ below $100\mathrm{K}$, indicating the possible importance of the electron-electron interaction in these borides. Superfluid density of $\mathrm{Zr}{\mathrm{B}}_{12}$ displays unconventional temperature dependence with pronounced shoulder at $T∕T_c$ equal to 0.65. Contrary to conventional theories we found a linear temperature dependence of $H_{c2}\left(T\right)$ for $\mathrm{Zr}{\mathrm{B}}_{12}$ from $T_c$ down to $0.35\mathrm{K}$. We suggest that both $\lambda \left(T\right)$ and $H_{c2}\left(T\right)$ dependencies in $\mathrm{Zr}{\mathrm{B}}_{12}$ can be explained by a two band BCS model with different superconducting gap and $T_c$.