Electron transport, penetration depth, and the upper critical magnetic field in ZrB12 and MgB2

Abstract

We report on the synthesis and measurements of the temperature dependence of resistivity, ρ(T ), the penetration depth, λ(T ), and upper critical magnetic field, Hc2(T ), for polycrystalline samples of dodecaboride ZrB12 and diboride MgB2. We conclude that ZrB12 as well as MgB2 behave like simple metals in the normal state with usual Bloch-Grüneisen temperature dependence of resistivity and with rather low resistive Debye temperature, TR = 280 K, for ZrB12 (as compared to MgB2 with TR = 900 K). The ρ(T ) and λ(T ) dependencies of these samples reveal a superconducting transition of ZrB12 at Tc = 6.0 K. Although a clear exponential λ(T ) dependence in MgB2 thin films and ceramic pellets was observed at low temperatures, this dependence was almost linear for ZrB12 below Tc/2. These features indicate s-wave pairing state in MgB2, whereas a d-wave pairing state is possible in ZrB12. A fit to the data gives a reduced energy gap 2∆(0)/kBTc = 1.6 for MgB2 films and pellets, in good agreement with published data for 3D π -sheets of the Fermi surface. Contrary to conventional theories we found a linear temperature dependence of Hc2(T ) (Hc2(0) = 0.15 T ) for ZrB12.

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

“…In our recent study of the electron transport and superconducting properties of polycrystalline ZrB 12 [15][16][17][18], we demonstrated that this compound behaves like a normal metal with the usual Bloch-Grüneisen dependence of ρ(T) but with rather low resistive Debye temperature (T R =280 K). The latter is almost three times smaller than Debye temperature obtained from C(T) data [19].…”

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

“…Different conclusions were obtained in the literature by assuming that the Debye temperature has a value between 270 and 300 K and remains constant at least up to 25 K. [13][14][15] The latter assumption is obviously not supported by specific-heat measurements ͑Fig. 4͒; the initial Debye temperature is close to 1000 K and the continuum approximation F͑͒ ϰ 2 does not hold beyond 10 K. At 25 K the deviation with respect to the initial C phonon ͑T͒ ϰ T 3 law is as high as 300%.…”

“…12 However PCS 11 and STS 12 rather indicate very strong coupling with a gap ratio 2⌬͑0͒ / k B T c = 4.8. The symmetry of the superconducting wave function appears to be d wave according to the temperature dependence of the penetration depth, 13 but s wave according to STS and PCS. 11,12 Similar discrepancies appear in the characterization of phonons.…”

“…12 Even the issue of type-I or type-II superconductivity is debated. 12,13 Some of these discrepancies were discussed in terms of surface superconductivity. 12 This situation motivated us to measure again the specific heat, a technique which, at variance with many experiments cited above, is a bulk probe sensitive to volume-averaged quantities.…”

“…11,12 Similar discrepancies appear in the characterization of phonons. The Debye temperature is reported to be D = 270-300 K according to transport, [13][14][15] but 930 K according to early specific-heat measurements. 3 Magnetic properties also are controversial: the upper critical field H c2 ͑0͒ is reported to be in the range of 1100 to over 2000 G according to PCS, radio-frequency susceptibility, and transport, 11,13 but only 390 G according to dc magnetization.…”