Optical properties of the iron arsenic superconductor ${\text{BaFe}}_{1.85}{\text{Co}}_{0.15}{\text{As}}_2$

The transport and complex optical properties of the electron-doped iron-arsenic superconductor ${\text{BaFe}}_{1.85}{\text{Co}}_{0.15}{\text{As}}_2$ with $T_c=25\text{K}$ have been examined in the Fe-As planes above and below $T_c$. A Bloch-Grüneisen analysis of the resistivity yields a weak electron-phonon coupling constant ${\lambda }_{ph}\simeq 0.2$. The low-frequency optical response in the normal state appears to be dominated by the electron pocket and may be described by a weakly interacting Fermi liquid with a Drude plasma frequency of ${\omega }_{p,D}\simeq 7840{\text{cm}}^{-1}$ $\left(\simeq 0.972\text{eV}\right)$ and scattering rate $1/{\tau }_D\simeq 126{\text{cm}}^{-1}$ $\left(\simeq 15\text{meV}\right)$ just above $T_c$. The frequency-dependent scattering rate $1/\tau \left(\omega \right)$ has kinks at $\simeq 12$ and 55 meV that appear to be related to bosonic excitations. Below $T_c$ the majority of the superconducting plasma frequency originates from the electron pocket and is estimated to be ${\omega }_{p,S}\simeq 5200{\text{cm}}^{-1}$ $\left({\lambda }_0\simeq 3000\text{Å}\right)$ for $T⪡T_c$, indicating that less than half the free carriers in the normal state have collapsed into the condensate, suggesting that this material is not in the clean limit. Supporting this finding is the observation that this material falls close to the universal scaling line for a Bardeen, Cooper, and Schrieffer dirty-limit superconductor in the weak-coupling limit. There are two energy scales for the superconductivity in the optical conductivity and photoinduced reflectivity at ${\Delta }_1\left(0\right)\simeq 3.1\pm 0.2\text{meV}$ and ${\Delta }_2\left(0\right)\simeq 7.4\pm 0.3\text{meV}$. This corresponds to either the gapping of the electron and hole pockets, respectively, or an anisotropic $s$-wave gap on the electron pocket; both views are consistent with the $s^{\pm }$ model.

Figure 1

(Color online) Temperature-dependent $ab$-plane resistivity of a ${\text{BaFe}}_{1.85}{\text{Co}}_{0.15}{\text{As}}_2$ single crystal with a superconducting transition at $T_c=25\text{K}$; the dashed curve is a Bloch-Grüneisen fit to the resistivity data (Sec. 3C). Insets: the unit cell of ${\text{BaFe}}_2{\text{As}}_2$ in the tetragonal $I4/mmm$ setting; detail of the resistivity in the region of $T_c$ illustrating the sharp transition width $\delta T_c\simeq 0.7\text{K}$.

Figure 2

(Color online) The temperature dependence of the reflectance of single-crystal ${\text{BaFe}}_{1.85}{\text{Co}}_{0.15}{\text{As}}_2$ for light polarized in the $a\text{−}b$ planes at several temperatures above and below $T_c$. There is a dramatic change in the reflectance below $T_c$. The “kinks” in low-temperature normal-state reflectivity (27 K) at $\simeq 12$ and 55 meV (marked by the two arrows at the inflection points in reflectivity) result from strong scattering of the carriers with some underlying bosonic excitations at these energy scales. Inset: the reflectance over a wide frequency range at 295 K.

Figure 3

(Color online) The real part of the optical conductivity of ${\text{BaFe}}_{1.85}{\text{Co}}_{0.15}{\text{As}}_2$ in the infrared region for light polarized in the $a\text{−}b$ planes at several temperatures above and below $T_c$. The extrapolated values for ${\sigma }_{\text{dc}}\equiv {\sigma }_1\left(\omega \to 0\right)$ agrees quite well with the dc transport data from Fig. 1 at 295 (●), 200 (◼), and 27 K (▲). Below $T_c$ there is a dramatic loss of low-frequency spectral weight due to the formation of a condensate. Inset: the conductivity at 295 and 27 K over a much wider frequency range.

Figure 4

(Color online) (a) The two-Drude and single Lorentz oscillator fit to the data at 27 K over a wide frequency range. The Drude responses can be characterized by narrow and broad bands with a single Lorentz oscillator centered at $\simeq 5200{\text{cm}}^{-1}$. (b) The fit to the data at 27 K using two Drude components and two Lorentz oscillators. A significant portion of the spectral weight of the broad Drude component has been transferred to the low-frequency Lorentz oscillator. The results of the fits are summarized in Table .

Figure 5

(Color online) The in-plane optical conductivity of the iron-arsenic superconductor ${\text{BaFe}}_{1.85}{\text{Co}}_{0.15}{\text{As}}_2$ $\left(T_c=25\text{K}\right)$ shown at 27 and 6 K (dashed and solid lines, respectively). (a) The optical conductivity with a single isotropic $s$-wave gap of ${\Delta }_0=3.1\text{meV}$ with a scattering rate $1/\tau =4{\Delta }_0$ is calculated for $T⪡T_c$ (long-dashed line) and superimposed on the contribution from the bound excitations in the mid-infrared (dotted line); the linear combination of the two curves (dotted-dashed line) does not reproduce the data well above $\approx 140{\text{cm}}^{-1}$. (b) The optical conductivity with isotropic $s$-wave gaps of ${\Delta }_1=3.1\text{meV}$ and ${\Delta }_2=7.4\text{meV}$ with the scattering rates $1/{\tau }_j=4{\Delta }_j$ is calculated for $T⪡T_c$ and superimposed on the Lorentzian contribution; the linear combination of the three curves is in much better agreement with the measured data.

Figure 6

(Color online) (a) The time evolution of the photoinduced reflectivity change, $\Delta R/R$, in ${\text{BaFe}}_{1.85}{\text{Co}}_{0.15}{\text{As}}_2$ as a function of temperature (below $T_c$) at 800 nm (the spectra are offset for clarity). (b) Temperature dependence of the relaxation time, ${\tau }_{fast}$. The inset shows the normalized amplitude $A_{fast}$. Solid lines are fits to the RT model, yielding ${\Delta }_2\approx 7.4\pm 1.2\text{meV}$. (c) Temperature dependence of the relaxation time, ${\tau }_{slow}$. The inset shows the normalized amplitude $A_{slow}$. Solid lines are fits to the RT model, yielding ${\Delta }_1\approx 3.5\pm 0.4\text{meV}$.

Figure 7

(Color online) The in-plane frequency-dependent scattering rate of ${\text{BaFe}}_{1.85}{\text{Co}}_{0.15}{\text{As}}_2$ for several temperatures above and below $T_c$ in the far-infrared region. The values for $1/{\tau }_D$ are shown at 295 K (●), 200 K (◼), and 27 K (▲), respectively, where the scattering rate displays little temperature dependence. The dashed lines at $\simeq 12$ and 55 meV indicate changes in the slope of $1/\tau \left(\omega \right)$. Inset: the frequency dependence of the effective mass.

Figure 8

(Color online) The log-log plot of the in-plane spectral weight of the superfluid density $N_c\equiv {\rho }_{s0}/8$ vs ${\sigma }_{\text{dc}}{T}_c$, for a variety of electron- and hole-doped cuprates compared with the result for ${\text{BaFe}}_{1.85}{\text{Co}}_{0.15}{\text{As}}_2$. The dashed line corresponds to the general result for the cuprates ${\rho }_{s0}/8\simeq 4.4{\sigma }_{\text{dc}}{T}_c$ while the dotted line is the result expected for a BCS dirty-limit superconductor in the weak-coupling limit, ${\rho }_{s0}/8\simeq 8.1{\sigma }_{\text{dc}}{T}_c$.