Specific heat, magnetic susceptibility, resistivity and thermal expansion of the superconductorZrB12

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 ZrB 12 , using well-characterized single crystals with a residual resistivity ratio Ͼ9. The specific heat gives the bulk result 2⌬͑0͒ / k B T c = 3.7 for the superconducting gap ratio, and excludes multiple gaps and d-wave symmetry for the Cooper pairs. The Sommerfeld constant ␥ n = 0.34 mJ K −2 gat −1 and the magnetic susceptibility = −2.1 ϫ 10 −5 indicate a low density of states at the Fermi level. The Debye temperature D is in the range 1000-1200 K near zero and room temperature, but decreases by a factor of ϳ2 at ϳ35 K. The specific heat and resistivity curves are inverted to yield approximations of the phonon density of states F͑͒ and the spectral electron-phonon scattering function ␣ tr 2 F͑͒, 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 T c establishes that the cell volume is nearly optimal with respect to T c .

Anomalous electron-phonon coupling probed on the surface of superconductorZrB12

“…[7]), and taking λ el−ph ≃ 0.67 [3], for the Grüniesen parameter we get the value γ ≃ 2.83. This value is in reasonable agreement with γ ≃ 3.3 obtained at a temperature slightly above T c by Lortz et al [4] based on thermal expansion measurements. PE on the electron-phonon coupling constant λ el−ph can be determined by using the well-known McMillan equation [20] …”

“…The field-cooled (FC) magnetization measurements were performed with a SQUID magnetometer in a field of 0.5 mT at temperatures between 1.75 K and 10 K. The absence of weak links between grains was confirmed by the linear magnetic field dependence of the FC magnetization, measured at 0.25 mT, 0.5 mT, and 1.0 mT for the highest and the lowest pressures at T = 1.75 K. dT c /dp = −0.0225(3) K/kbar. Note that this value is in good agreement with dT c /dp ≃ −0.024 K/kbar obtained indirectly by Lortz et al [4] from thermal expansion measurements.…”

“…Among BCS superconductors the zirconium dodecaboride (ZrB 12 ) is probably a candidate for the observation of such type of anomalous coupling. It stems from the rather small value of the Fermi energy ∼1 eV [3] that, together with the Debye temperature ∼20 meV [4], leads to a ratio ω 0 /E f ∼0.02. A strong coupling ratio 2∆/k B T c ≃ 4.8 was observed by surface sensitive techniques [3,6].…”

“…A slightly larger value d ln λ el−ph /dp = −0.22%/kbar is obtained with γ = 3.3 from the Ref. [4]. As a next step we studied the pressure effect on the magnetic field penetration depth λ.…”

“…[2] that nonadiabatic character can be further enhanced by low charge carrier density, that is the case for ZrB 12 [4,5].…”