Weak-coupling superconductivity in electron-doped NaFe${}_{0.95}$Co${}_{0.05}$As revealed by ARPES

We report a systematic study on the electronic structure and superconducting (SC) gaps in electron-doped NaFe${}_{0.95}$Co${}_{0.05}$As superconductor using angle-resolved photoemission spectroscopy. Holelike Fermi sheets are at the zone center and electronlike Fermi sheets are at the zone corner, and are mainly contributed by $xz$ and $yz$ orbital characters. Our results reveal a $\frac{\Delta }{K_B{T}_c}$ in the range of 1.8–2.1, suggesting a weak-coupling superconductivity in these compounds. Gap closing above the transition temperature ($T_c$) shows the absence of pseudogaps. Gap evolution with temperature follows the BCS gap equation near the $\Gamma$, $Z$, and $M$ high symmetry points. Furthermore, an almost isotropic superconductivity along the $k_z$ direction in the momentum space is observed by varying the excitation energies.

Figure 1

(a) is the FS map taken in the $k_x-k_y$ plane measured using $s$-polarized light with an excitation energy $h\nu =80$ eV, and inset is the map around $\Gamma$ taken at 30 meV below the Fermi level ($E_F$). (b) and (c) are the energy distribution map (EDM) cuts taken at $\Gamma$ (along the direction shown on FS map) measured using $p$- and $s$-polarized lights, respectively. (d) is EDM cut taken at the $M$-point. Dashed lines on the EDMs are guides to the eye, representing electronic band dispersions. (e), (f), and (g) are the energy distribution curves (EDCs) of EDMs shown in (b), (c), and (d), respectively. (h) is the FS map taken in the $k_{\parallel }-k_z$ plane measured using $p$-polarized light. (i) and (k) show the resultant EMDs from the addition of EDMs measured using $s$- and $p$-polarized light taken at $k_z=0$ and $\pi$ at the zone center, respectively. (j) and (l) are the respective second derivatives of the EDMs show in (i) and (k). In the figure $p$- and $s$-polarized photons are indicated by double circles and double sided arrow, respectively.

Figure 2

Top panel shows the EDMs measured with an excitation energy $h\nu =20$ eV when the sample is in normal state ($T=23$ K). Bottom panel shows second derivatives of the respective EDMs.

Figure 3

Integrated energy distribution curves (IEDCs) of the band ${\alpha }_2$ as a function of temperature measured with photon energy 20 eV (a), 27 eV (b), and 39 eV (c). (d) shows the IEDCs as a function of excitation energy measured at a sample temperature of 1 K. Solid curves in figure represent Dynes function fitting to the IEDCs (see text). (e) shows the ranges of momentum integration (red blocks) used to extract the EDCs shown in (a), (b) and (c)

Figure 4

IEDCs are taken as a function temperature for the band $\beta$ measured with photon energy 20 eV (a) and 23 eV (b). Insets in (a) and (b) show the range of momentum integration (red block) used to extract the EDCs. (c) is SC gap evolution with temperature measured at various photon energies for the band ${\alpha }_2$. (d) is the same as (c) but taken from the band $\beta$.

Figure 5

(a) Symmetrized IEDCs of the band ${\alpha }_2$ measured with the photon energy 20 eV. (b) SC gap evolution with temperature exctracetd from (a). (c) Single-particle scattering rates as a function of temperature.