Specific-Heat Study of Superconducting and Normal States in FeSe_1-xTe_x (0.6≤x ≤1) Single Crystals: Strong-Coupling Superconductivity, Strong Electron-Correlation, and Inhomogeneity

Abstract

The electronic specific heat of as-grown and annealed single-crystals of FeSe 1-x Te x (0.6 ≤ x ≤ 1) has been investigated. It has been found that annealed single-crystals with x = 0.6 -0.9 exhibit bulk superconductivity with a clear specific-heat jump at the superconducting (SC) transition temperature, T c . Both 2Δ 0 /k B T c [Δ 0 : the SC gap at 0 K estimated using the single-band BCS s-wave model]and ⊿C/(γ n -γ 0 )T c [⊿C: the specific-heat jump at T c , γ n : the electronic specific-heat coefficient in the normal state, γ 0 : the residual electronic specific-heat coefficient at 0 K in the SC state] are largest in the well-annealed single-crystal with x = 0.7, i.e., 4.29 and 2.76, respectively, indicating that the superconductivity is of the strong coupling. The thermodynamic critical field has also been estimated. γ n has been found to be one order of magnitude larger than those estimated from the band calculations and increases with increasing x at x = 0.6 -0.9, which is surmised to be due to the increase in the electronic effective mass, namely, the enhancement of the electron correlation. It has been found that there remains a finite value of γ 0 in the SC state even in the well-annealed single-crystals with x = 0.8 -0.9, suggesting an inhomogeneous electronic state in real space and/or momentum space.

Strong-coupling superconductivity in NaFe1−xCoxAs: Validity of Eliashberg theory

“…(1) and (2). The thermodynamic properties of the Fe-based superconductors have been measured in many systems [10][11][12][13][14][15][16][17][18][19][20][21] . In Ba 0.6 K 0.4 Fe 2 As 2 , a calculation based on the Eliashberg model considering multiple bands is able to quantitatively reproduce the experimental results based on the assumption that spin fluctuations are electron pairing mediating bosons 13 .…”

Electronic specific heat inBaFe2−xNixAs2

“…The most important parameter is γ n = C/T , which is proportional to the density of states at the Fermi energy and the effective electron mass. The measurements in the iron-based superconductors have given a variety of values of γ n for different materials [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . A detailed study on the Ba(Fe 1−x Co x ) 2 As 2 shows that γ n becomes maximum at optimal doping 4,7 , suggesting the influence of the antiferromagnetic (AF) order that disappears at the same doping 17 .…”

“…To reveal the electronic specific heat, one may try to fit the data above T c with certain functions 2,3 or find a reference sample without superconductivity by assuming that the specific heat of phonons change little with doping 4,5 . In the latter case, the specific heat of the phonons of the reference sample may be simply adjusted as aC phonon (bT ) with a and b as the tuning parameters (a-b method) to account for the change of the phonon spectra with doping [6][7][8][10][11][12][13][14]16 . In most cases, a linear temperature dependence of the electronic specific heat below T c is assumed to account for the entropy conservation, i.e., γ n is temperature-independent.…”

Dynamics and mechanism of oxygen annealing in Fe1+yTe0.6Se0.4 single crystal

“…Recently, London penetration depth measurement down to 50 mK indicates a possible nodal gap21. On the other hand, although Liu et al 14 reported that bulk superconductivity resides only in the region of Se level higher than 29%, it was observed in the Se doping level between 10 and 50% by Noji et al 2223. As for the Hall coefficient, conflicting low-temperature behaviors have been observed in crystals with nominally the same amount of Se242526.…”