Doping-dependent superconducting physical quantities of K-doped BaFe$_2$As$_2$ obtained through infrared spectroscopy

We investigated four single crystals of K-doped BaFe$_2$As$_2$ (Ba-122), Ba$_{1-x}$K$_x$Fe$_2$As$_2$ with $x$ = 0.29, 0.36, 0.40, and 0.51, using infrared spectroscopy. We explored a wide variety of doping levels, from under- to overdoped. We obtained the superfluid plasma frequencies ($\Omega_{\mathrm{sp}}$) and corresponding London penetration depths ($\lambda_{\mathrm{L}}$) from the measured optical conductivity spectra. We also extracted the electron-boson spectral density (EBSD) functions using a two-parallel charge transport channel approach in the superconducting (SC) state. From the extracted EBSD functions, the maximum SC transition temperatures ($T_c^{\mathrm{Max}}$) were determined using a generalized McMillan formula and the SC coherence lengths ($\xi_{\mathrm{SC}}$) were calculated using the timescales encoded in the EBSD functions and reported Fermi velocities. We identified some similarities and differences in the doping-dependent SC quantities between the K-doped Ba-122 and the hole-doped cuprates. We expect that the various SC quantities obtained across the wide doping range will provide helpful information for establishing the microscopic pairing mechanism in Fe-pnictide superconductors.