Specific heat, magnetic susceptibility, resistivity and thermal expansion of the superconductor ZrB12

TL;DR

This study provides comprehensive measurements of thermodynamic and electronic properties of ZrB12, clarifying its superconducting gap, phonon modes, and electron-phonon interactions, resolving previous conflicting data.

Contribution

It offers new, detailed experimental data on ZrB12's properties, including specific heat, resistivity, and phonon spectra, and clarifies the nature of its superconducting gap and phonon modes.

Findings

Superconducting gap ratio 2*delta(0)/(k_B*Tc)=3.7, excludes multiple gaps and d-wave symmetry.

Identifies a 15 meV phonon mode related to Zr vibrations in B cages, contributing to electron-phonon coupling.

Debye temperature ranges from 1000-1200 K, decreasing at low temperatures.

Abstract

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.