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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, usinginfrared 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. Wealso extracted the electron-boson spectral density (EBSD) functions using atwo-parallel charge transport channel approach in the superconducting (SC)state. From the extracted EBSD functions, the maximum SC transitiontemperatures ($T_c^{\mathrm{Max}}$) were determined using a generalizedMcMillan formula and the SC coherence lengths ($\xi_{\mathrm{SC}}$) werecalculated using the timescales encoded in the EBSD functions and reportedFermi velocities. We identified some similarities and differences in thedoping-dependent SC quantities between the K-doped Ba-122 and the hole-dopedcuprates. We expect that the various SC quantities obtained across the widedoping range will provide helpful information for establishing the microscopicpairing mechanism in Fe-pnictide superconductors.

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