Optical Spectroscopy of Superconducting ${\mathrm{Ba}}_{0.55}{\mathbf{K}}_{0.45}{\mathrm{Fe}}_2{\mathrm{As}}_2$: Evidence for Strong Coupling to Low-Energy Bosons

Normal state optical spectroscopy on single crystals of the new iron arsenide superconductor ${\mathrm{Ba}}_{0.55}{\mathrm{K}}_{0.45}{\mathrm{Fe}}_2{\mathrm{As}}_2$ shows that the infrared spectrum consists of two major components: a strong metallic Drude band and a well-separated midinfrared absorption centered at 0.7 eV. It is difficult to separate the two components unambiguously but several fits using Lorentzian peaks suggest a model with a Drude peak having a plasma frequency of 1.6 to 2.1 eV and a midinfrared peak with a plasma frequency of 2.5 eV. Detailed analysis of the frequency dependent scattering rate shows that the charge carriers interact with a broad bosonic spectrum extending beyond 100 meV with a very large coupling constant $\lambda =3.4$ at low temperature. As the temperature increases this coupling weakens to $\lambda =0.78$ at ambient temperature. This suggests a bosonic spectrum that is similar to what is seen in the lower $T_c$ cuprates.

Figure 1

The reflectance of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ as a function of incident photon energy at nine temperatures. The inset shows the reflectance at room temperature in a wider range of energies. There is a sharp break in the monotonic linear decay of reflectance at 0.5 eV signaling the presence of a strong midinfrared band. Also shown is the reflectance of a typical high temperature superconductor. The break at 0.5 eV is absent in this material and the strong linear decay of reflectance persists up to 1.2 eV.

Figure 2

The optical conductivity as a function of photon energy for four temperatures ordered from top 295 K to bottom 28 K at the position of the arrow. The inset shows the low frequency region on an expanded scale.

Figure 3

Scattering rate $1/\tau (\omega )$ vs photon energy in the region below 140 meV at four temperatures (curves showing noise fluctuations) and maximum entropy calculations based on Eq. (2), using the bosonic functions shown in Fig. 4 (smooth curves).

Figure 4

Bosonic functions ${\alpha }^{2}F(\omega )$ extracted from the optical scattering rates of Fig. 3 using a maximum entropy inversion of Eq. (2). The inset is the calculated electron-phonon ${\alpha }^{2}F(\Omega )$ calculated by Boeri et al. with $\lambda =0.21$.

Figure 5

The temperature dependence of the mass renormalization parameter $\lambda =2\int d\Omega {\alpha }^{2}F(\Omega )/\Omega$ based on the ${\alpha }^{2}F(\Omega )$ of Fig. 4.