Penetration depth of Ba1−xKxFe2As2 single crystals explained within a multiband Eliashberg s± approach

Abstract

We investigate the penetration depth of high-quality ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ single crystals by a planar waveguide resonator technique, in a cavity perturbation approach. The experimental ${\ensuremath{\lambda}}_{L}$ is compared to calculations based on the three-band Eliashberg equations within the $s\ifmmode\pm\else\textpm\fi{}$ wave model. To this end, the anisotropy of the penetration depth is taken into account. In fact, the agreement between theory and experiment is remarkable. The low-temperature value of the in-plane penetration depth, ${\ensuremath{\lambda}}_{L,ab}(5\phantom{\rule{4.pt}{0ex}}\text{K})=220\phantom{\rule{4pt}{0ex}}\mathrm{nm}$, and the total plasma frequency, ${\ensuremath{\omega}}_{p}=1.0\phantom{\rule{4pt}{0ex}}\mathrm{eV}$, are also consistent with earlier results. This overall consistency validates the model itself, thus allowing us to estimate parameters that are missing in literature, such as the plasma frequency for each band: it turns out that ${\ensuremath{\omega}}_{p,1}={\ensuremath{\omega}}_{p,3}=0.32\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ and ${\ensuremath{\omega}}_{p,2}=0.89\phantom{\rule{4pt}{0ex}}\mathrm{eV}$, with the subscripts 1 and 2 denoting the two hole bands and 3 the equivalent electron band.