Specific heat, magnetic susceptibility, resistivity and thermal   expansion of the superconductor ZrB12
  In an attempt to clarify conflicting published data, we report new measurements of specific heat, resistivity, magnetic susceptibility, and thermal expansivity up to room temperature for the 6 K superconductor ZrB12, using well-characterized single crystals with a residual resistivity ratio >9. The specific heat gives the bulk result 2*delta(0)/(k_B*Tc)=3.7 for the superconducting gap ratio, and excludes multiple gaps and d-wave symmetry for the Cooper pairs. The Sommerfeld constant gamma_n = 0.34 mJ K-2 gat-1 and the magnetic susceptibility xsi = -2.1 x 10^-5 indicate a low density of states at the Fermi level. The Debye temperature theta_D is in the range 1000-1200 K near zero and room temperature, but decreases by a factor of ~2 at ~35 K. The specific heat and resistivity curves are inverted to yield approximations of the phonon density of states F(omega) and the spectral electron-phonon scattering function alpha_tr^2 F(omega), respectively. Both unveil a 15 meV mode, attributed to Zr vibrations in oversized B cages, which gives rise to electron-phonon coupling. The thermal expansivity further shows that this mode is anharmonic, while the vanishingly small discontinuity at Tc establishes that the cell volume is nearly optimal with respect to Tc. 
R. Lortz, Y. Wang, S. Abe, C. Meingast, Yu. B. Paderno, V. Filippov,   A. Junod