Calorimetric evidence of strong-coupling multiband superconductivity in Fe(Te${}_{0.57}$Se${}_{0.43}$) single crystal

We have investigated the specific heat of optimally doped iron chalcogenide superconductor Fe(Te${}_{0.57}$Se${}_{0.43}$) with a high-quality single crystal sample. The electronic specific heat $C_{\mathrm{e}}$ of this sample has been successfully separated from the phonon contribution using the specific heat of a nonsuperconducting sample (Fe${}_{0.90}$Cu${}_{0.10}$)(Te${}_{0.57}$Se${}_{0.43}$) as a reference. The normal-state Sommerfeld coefficient ${\gamma }_{\mathrm{n}}$ of the superconducting sample is found to be $~$26.6 mJ/mol ${\mathrm{K}}^2$, indicating intermediate electronic correlation. The temperature dependence of $C_{\mathrm{e}}$ in the superconducting state can be best fitted using a double-gap model with $2{\Delta }_s(0)/k_B{T}_{\mathrm{c}}=3.92$ and $2{\Delta }_l(0)/k_B{T}_{\mathrm{c}}=5.84$. The large gap magnitudes derived from fitting, as well as the large specific heat jump of $\Delta C_{\mathrm{e}}(T_{\mathrm{c}})/{\gamma }_{\mathrm{n}}{T}_{\mathrm{c}}~2.11$, indicate strong-coupling superconductivity. Furthermore, the magnetic field dependence of specific heat shows strong evidence for multiband superconductivity.

Figure 1

(a) Temperature dependence of dc susceptibility measured with a magnetic field of 30 Oe (applied along the $c$ axis) and zero-field-cooling history; (b) in-plane resistivity as a function of temperature. SC and reference represent Fe(Te${}_{0.57}$Se${}_{0.43}$) and (Fe${}_{0.90}$Cu${}_{0.10}$)(Te${}_{0.57}$Se${}_{0.43}$) samples, respectively.

Figure 2

Temperature dependence of specific heat $C(T)/T$ for SC and reference samples. Left inset: $C(T)/T$ versus $T^2$ at low temperature for both samples. The solid line shows the linear fit to $C(T)/T=\gamma +\beta T^2$. Right inset: Specific jump $\Delta C(T_{\mathrm{c}})/T_{\mathrm{c}}$ evaluated from the isoentropic construction.

Figure 3

Electronic specific heat $C_{\mathrm{e}}(T)/T$ as a function of temperature for Fe(Te${}_{0.57}$Se${}_{0.43}$) (The data have been subtracted by the normal-state Sommerfeld coefficient ${\gamma }_{\mathrm{n}}$ (≈ 26.6 mJ/mol ${\mathrm{K}}^2$, see text). The solid and dashed lines represent the phenomenological two-band model fit and the BCS single-band model fit, respectively. The inset shows a difference between the single- and two-band fits.

Figure 4

(a) Low temperature specific heat $C/T$ as a function of $T^2$ under various magnetic fields applied along the crystalline $c$ axis for Fe(Te${}_{0.57}$Se${}_{0.43}$). The solid lines represent the linear fit to $C/T=\gamma +\beta T^2$. (b) Magnetic-field-induced change in the specific heat at 3.0 K, normalized to ${\gamma }_{\mathrm{n}}-{\gamma }_{\mathrm{res}}$ where ${\gamma }_{\mathrm{n}}$ and ${\gamma }_{\mathrm{res}}$, respectively, represent the normal-state Sommerfeld coefficient (≈26.6 mJ/mol ${\mathrm{K}}^2$) and the coefficient of residual electronic specific heat (≈2.3 mJ/mol ${\mathrm{K}}^2$, see text). $H/H_{c2}(0)$ represents the reduced field, where $H_{c2}(0)=48$ T, quoted from Ref. 40. The diamond symbol represents the $\Delta \gamma (H)$ data reported by Klein et al.[50] The dashed and doted lines represent the field dependence of $\Delta \gamma$ expected for the standard $s$-wave pairing and the clean $d$-wave pairing, respectively.