Two-band Bardeen-Cooper-Schrieffer superconducting state of the iron pnictide compound Ba(Fe${}_{0.9}$Co${}_{0.1}$)${}_2$As${}_2$

The optical conductivity and permittivity spectra of Ba(Fe${}_{0.9}$Co${}_{0.1}$)${}_2$As${}_2$ films ($T_c=20\hspace{0.5em}\text{K}$) are analyzed together with the literature data on photoemission and specific heat. In the superconducting state at all temperatures up to $T_c$ the temperature dependence of the magnetic field penetration depth is well described within the generalized two-band BCS model with intraband and interband pairing interactions considered. It is shown that the small superconducting energy gap $2{\Delta }^{(1)}=3.7\text{meV}$ develops in the electron subsystem while the larger gap $2{\Delta }^{(2)}=7.9\text{meV}$ opens in the hole subsystem. The normal state parameters, such as plasma frequency and scattering rate, of electron and hole conduction bands are determined.

Figure 1

(a) Reflectivity of a Ba(Fe${}_{0.9}$Co${}_{0.1}$)${}_2$As${}_2$ film on a (La,Sr)(Al,Ta)O${}_3$ substrate in the normal ($T=30$ K, open dots) and superconducting state ($T=5$ K, black dots) (Ref. 17). The gray solid line is a fit to the 30 K reflectivity using the conductivity presented in panel (b). Black solid line describes the reflectivity in the SC state ($T=5$ K) with the conductivity and permittivity shown in Fig. 2. (b) Optical conductivity of Ba(Fe${}_{0.9}$Co${}_{0.1}$)${}_2$As${}_2$ at $T=30$ K (thick line) with the free-carrier contribution of electrons and holes and resonance absorptions in the midinfrared.

Figure 2

Frequency-dependent (a) conductivity and (b) permittivity of Ba(Fe${}_{0.9}$Co${}_{0.1}$)${}_2$As${}_2$ in the superconducting state ($T=5$ K) (Ref. 17). Dots correspond to directly measured data. The thin lines show contributions from electron and hole (A and B according to Ref. 19) bands calculated within the BCS model (Ref. 29) while the thick lines are the total contributions of electrons and holes. The gray area indicates uncertainty which amounts from the reflectivity fit [Fig. 1a] and directly measured values of THz conductivity and permittivity. The dotted line corresponds to the normal-state conductivity at $T=30\text{K}$.

Figure 3

Temperature dependences of (a) penetration depth and (b) energy gaps in electronic and hole bands of Ba(Fe${}_{0.9}$Co${}_{0.1}$)${}_2$As${}_2$. Dots correspond to experimental data (Ref. 17). Lines are calculations according to extended BCS two-band model with electron-boson coupling constants: intraband $\lambda =0.45$; interband ${\lambda }_{12}=0.1$. The dashed lines: (a) penetration depth coming from electron and hole bands and calculated within the $\alpha$-approximation (Ref. 29) of the BCS model; (b) the gap in the electronic subsystem within the $\alpha$ approximation. Dotted line in panel (b) shows the temperature dependence the electronic gap would have without interband coupling.