Specific Heat of Ba_0.59K_0.41Fe₂As₂, an Fe-Pnictide Superconductor with T_c = 36.9 K, and a New Method for Identifying the Electron Contribution

Abstract

We report measurements of the specific heat of Ba 0.59 K 0.41 Fe 2 As 2 , an Fe-pnictide superconductor with T c = 36.9 K, for which there are suggestions of an unusual electron pairing mechanism. We use a new method of analysis of the data to derive the parameters characteristic of the electron contribution. It is based on comparisons of α-model expressions for the electron contribution with the total specific heat, which give the electron contribution directly. It obviates the need in the conventional analyses for an independent, necessarily approximate, determination of the lattice contribution, which is subtracted from the total specific heat to obtain the electron contribution. It eliminates the uncertainties and errors in the electron contribution that follow from the approximations in the determination of the lattice contribution. Our values of the parameters characteristic of the electron contribution differ significantly from those obtained in conventional analyses of specific-heat data for five similar holedoped BaFe 2 As 2 superconductors, which also differ significantly among themselves. For Ba 0.59 K 0.41 Fe 2 As 2 the electron density of states is comprised of contributions from two electron bands with superconducting-state energy gaps that differ by a factor 3.8, with 77% coming from the band with the larger gap. The variation of the specific heat with magnetic field is consistent with extended s-wave pairing, one of the theoretical predictions. The relation between the densities of states and the energy gaps in the two bands is not consistent with a theoretical model based on interband interactions alone. Comparison of the normal-state density of states with band-structure calculations shows an extraordinarily large effective mass 2 enhancement, for which there is no precedent in similar materials and no theoretical explanation.

Method for Accurate Determination of the Electron Contribution: Specific Heat of Ba0.59K0.41Fe2As2

“…In comparison with other measurements on similar materials the transition is relatively sharp and the discontinuities are relatively large, e.g., although ΔC e (T c )/T c seems to be similar to that found in one of the five measurements on similar materials (described in Sect. 6 of [4]) it is clearly larger than those in the other four.…”

“…These results show the existence of a small-gap band characterized by the parameters α 2 ¼ 0.86 and γ n2 ¼ (337 AE 17)/36.9 ¼ 9.1 AE 0.5 mJ K À2 mol À1 . Because of the small value of γ n2 , and particularly the small value of α 2 , this band makes only small contributions to the discontinuities at T c : [4]) and the comparison suggests some consideration of the uncertainties: A quantitative measure of the uncertainty in our value of γ n2 is given directly by the fit, γ n2 ¼ 9.…”

“…[As noted in the Introduction, some of the measurements on other near-optimally hole-doped 122 Fe-pnictide superconductors (described in more detail in Sect. 6 of [4]) showed evidence of two gaps, and the details and references are given in Table 23.2.] The total DOS, as measured by the coefficient of the electron contribution to the specific heat, corresponds to γ n ¼ 40.1 mJ K À2 mol À1 , and it is comprised of a contribution, γ n1 ¼ 31.0 mJ K À2 mol À1 , from the band with the larger gap, Δ 1 (0) ¼ 10.49 meV, and a contribution, γ n2 ¼ 9.1 mJ K À2 mol À1 , from the band with the smaller gap, Δ 2 (0) ¼ 2.73 meV.…”

“…In the special case of a C lat that is determined in a high-temperature fit to normal-state data and then extrapolated to low temperatures, imposition of the entropyconservation constraint can reduce gross errors in the derived C lat (a detailed analysis is presented in Sect. 6 of [4]). More generally however, its effect is limited by the small fraction of the entropy at T c that is electron entropy, e.g.,~13% in the results reported here.…”

“…The analysis of the C data should give the conductionelectron density of states (DOS) and the values of the energy gaps in the superconducting state, but the conventional analyses gives a variety of results for these parameters in similar materials that reflect the errors in the approximations for C lat . Recently we recognized that the α model, which gives a good representation of C es , offers a way out of this dilemma: We showed that C es for Ba 0.59 K 0.41 Fe 2 As 2 could be extracted directly from the total C data by using α-model expressions for C es , bypassing the need for an independent determination of C lat [4]. That paper included discussions of C lat , its proper mathematical representations in different temperature regions, the approximations used in the conventional analyses, and a comparison of our results for Ba 0.59 K 0.41 Fe 2 As 2 with those obtained by conventional analyses of specific-heat data on similar materials as well as with results obtained by ARPES.…”