Eliashberg approach to infrared anomalies induced by the superconducting state of Ba${}_{0.68}$K${}_{0.32}$Fe${}_2$As${}_2$ single crystals

We report the full complex dielectric function of high-purity ${\text{Ba}}_{0.68}{\text{K}}_{0.32}{\text{Fe}}_2{\text{As}}_2$ single crystals with $T_{\mathrm{c}}=38.5\text{K}$ determined by wideband spectroscopic ellipsometry at temperatures $10\le T\le 300\text{K}$. We discuss the microscopic origin of superconductivity-induced infrared optical anomalies in the framework of a multiband Eliashberg theory with two distinct superconducting gap energies, $2{\Delta }_{\mathrm{A}}\approx 6k_{\mathrm{B}}{T}_{\mathrm{c}}$ and $2{\Delta }_{\mathrm{B}}\approx 2.2k_{\mathrm{B}}{T}_{\mathrm{c}}$. The observed unusual suppression of the optical conductivity in the superconducting state at energies up to $14k_{\mathrm{B}}{T}_{\mathrm{c}}$ can be ascribed to spin-fluctuation–assisted processes in the clean limit of the strong-coupling regime.

Figure 1

Real part of the (a) optical conductivity and (b) dielectric function in the far-infrared spectral region. Two characteristic superconductivity energy scales are present: 6 and $14k_{\mathrm{B}}{T}_{\mathrm{c}}$. Inset: Temperature dependence of the normalized inverse penetration depth obtained via a Kramers-Kronig consistency procedure.

Figure 2

Real part of the (a) optical conductivity and (b) dielectric function of ${\text{Ba}}_{0.68}{\text{K}}_{0.32}{\text{Fe}}_2{\text{As}}_2$ at 300 K (red line, far left) and 10 K (blue line). Interband transitions inferred from the dispersion analysis (solid black lines).

Figure 3

Optical scattering rate obtained from the experimental data at 41 and $10\text{K}$ within the extended Drude model, with the contribution of the interband transitions subtracted [blue (dark gray) and black lines, respectively] and at $41\text{K}$ without subtraction [green (light gray) line]. Dash-dotted line indicates the saturation level of the high-energy optical scattering rate.

Figure 4

(a) Real part of the optical conductivity at 41 K [blue (gray) line]. The contribution of itinerant charge carriers [blue (upper) area] is obtained by subtracting all interband transitions ${\sigma }_1^{\mathrm{inter}}\left(\omega \right)$ [gray (lower) area] from the optical response. (b) Real part of the dielectric function at 41 K [blue (gray) line]. The free-charge-carrier response ${\varepsilon }_1^{\mathrm{it}}\left(\omega \right)$ (open circles) is obtained by eliminating all interband transitions ${\varepsilon }_1^{\mathrm{inter}}\left(\omega \right)$ (black solid line). The blue dashed line indicates the screened plasma frequency at 41 K.

Figure 5

Temperature dependence of the (a) free energy and (b) superconducting gaps in the four-band (lines) and reduced two-band (symbol) models, with coupling matrices given by Eqs. (2) and (7), respectively.

Figure 6

(a) Real part of the far-infrared conductivity obtained within the two-band Eliashberg theory (see text) at $40\text{K}$ [blue (gray) lines] and $10\text{K}$ (black lines) in the clean limit ${\gamma }_{\mathrm{A}}={\gamma }_{\mathrm{B}}=1{\text{cm}}^{-1}$ (solid lines) and dirty limit ${\gamma }_{\mathrm{A}}={\gamma }_{\mathrm{B}}=200{\text{cm}}^{-1}$ (dashed lines). (b) Optical scattering rate in the clean limit of the same model. The gray area shows the normalized boson spectral function $B\left(\omega \right)$ used in the calculation, displaced from zero by $2{\Delta }_{\mathrm{A}}$ to assist interpretation in the superconducting state.[31]