Two-band BCS mechanism of superconductivity in a Ba(Fe$_{0.9}$Co$_{0.1}$)$_2$As$_2$ high-temperature superconductor

Terahertz and infrared spectra of the conductivity, $\sigma(\nu)$, and dielectric constant, $\varepsilon(\nu)$, of a Ba(Fe$_{0.9}$Co$_{0.1}$)$_2$As$_2$ film ($T_c=20\,$К) have been analyzed together with previous specific-heat and angular resolved photoelectron spectroscopy data. It has been shown that the spectra $\sigma(\nu)$ and $\varepsilon(\nu)$ of Ba(Fe$_{0.9}$Co$_{0.1}$)$_2$As$_2$ in the superconducting phase at $T=5$ К, as well as the magnetic field penetration depth, can be described well using the standard Bardeen-Cooper-Schrieffer (BCS) model with an additive contribution of electron and hole bands. It has been found that the measured temperature dependence of the magnetic field penetration depth in a wide temperature range $5$ K${}<T<T_c$ can be described only with the introduction of interband pairing interaction. The coupling constant of electron and hole bands, $\lambda_{1,2}=0.1$, as well as the temperature dependences of superconducting gaps in the electron and hole subsystems, has been determined using the model of two-band superconductivity developed earlier for MgB$_2$.