Nodes in the order parameter of superconducting iron pnictides investigated by infrared spectroscopy

The temperature and frequency dependences of the conductivity derived from optical reflection and transmission measurements of electron-doped ${\text{BaFe}}_2{\text{As}}_2$ crystals and films are analyzed according to gap nodes or possibly a very small gap, or in the crossover region between these two possibilities. This can arise when one of the several pockets known to exist in these systems has extended $s$-wave gap symmetry with an anisotropic piece cancelling or nearly so the isotropic part in some momentum direction. Alternatively, a node can be lifted by impurity scattering which reduces anisotropy. We find that the smaller gap on the hole pocket at the $\Gamma$ point in the Brillouin zone is isotropic $s$ wave while the electron pocket at the $M$ point has a larger gap which is anisotropic and falls in the crossover region.

Figure 1

(Color online) The optical properties of $\text{Ba}{\left({\text{Fe}}_{0.92}{\text{Co}}_{0.08}\right)}_2{\text{As}}_2$ and $\text{Ba}{\left({\text{Fe}}_{0.95}{\text{Ni}}_{0.05}\right)}_2{\text{As}}_2$ at selected temperatures: (a) and (c) Reflectivity; (b) and (d) Real part of the optical conductivity from 25 to 250 ${\text{cm}}^{-1}$.

Figure 2

(Color online) Relative change in the optical properties of $\text{Ba}{\left({\text{Fe}}_{0.92}{\text{Co}}_{0.08}\right)}_2{\text{As}}_2$ upon entering the superconducting state at $T_c=25\text{K}$. The solid lines correspond to experimental data obtained at $T=10$, 15, and 20 K, normalized to the 30 K data. The dashed lines represent fits by a two-gap model with different symmetry, where the first gap $2{\Delta }_0^{\left(1\right)}=5\text{meV}$ has a simple $s$-wave symmetry while the second gap exhibits $s+d$ wave symmetry with 37% $s$-wave character and an amplitude $2{\Delta }_0^{\left(2\right)}=15\text{meV}$. The elastic-scattering rate used here is $\hslash {\tau }_{\text{imp}}^{-1}=31.4\text{meV}$. (a) Reflectivity $R\left(\omega ,T\right)/R\left(\omega ,T=30\text{K}\right)$, (b) optical conductivity ${\sigma }_1\left(\omega ,T\right)/{\sigma }_1\left(\omega ,T=30\text{K}\right)$, and (c) frequency dependent optical scattering rate ${\tau }^{-1}\left(\omega ,T\right)/{\tau }^{-1}\left(\omega ,T=30\text{K}\right)$. The inset sketches the two Fermi-surface pockets in $k$ space with an isotropic $s$-wave gap about $\Gamma$ and an anisotropic extended $s$-wave gap about $M$.

Figure 3

(Color online) (a) The real part of the optical conductivity ${\sigma }_1\left(\omega \right)$ in meV vs the photon energy $\hslash \omega$ in meV for an $s+d$-wave model at $T=1.25\text{K}$ and for various values of the parameter $x$ which multiplied by 100 gives the percentage of the $s$-wave admixture. Thus, $x=0$ corresponds to pure $d$-wave symmetry of the gap while $x=1$ corresponds to $s$-wave symmetry. ${\Delta }_0=7.5\text{meV}$ and the elastic-scattering rate $\hslash {\tau }_{\text{imp}}^{-1}=31.4\text{meV}$. The $x=0.37$ corresponds to the $s$-wave admixture used in the analysis presented in Fig. 1. (b) The same as (a) but for the normalized real part of the optical conductivity ${\sigma }_1\left(\omega \right)/{\sigma }_1\left(\omega ,T=30\text{K}\right)$ with ${\sigma }_1\left(\omega ,T=30\text{K}\right)$ its normal-state value. (c) The same as (a) but for the normalized optical scattering rate ${\tau }^{-1}\left(\omega \right)/{\tau }^{-1}\left(\omega ,T=30\text{K}\right)$.

Figure 4

(Color online) Relative change in the optical properties of $\text{Ba}{\left({\text{Fe}}_{0.95}{\text{Ni}}_{0.05}\right)}_2{\text{As}}_2$ upon entering the superconducting state at $T_c=20\text{K}$. The solid lines correspond to experimental data obtained at $T=9$ and 14 K. The dashed lines represent fits by a two-gap model with different symmetry, where the first gap $2{\Delta }_0^{\left(1\right)}=4.5\text{meV}$ has a simple $s$-wave symmetry while the second gap exhibits $s+d$ wave symmetry with 24% $s$-wave character and an amplitude $2{\Delta }_0^{\left(2\right)}=14\text{meV}$. (a) Reflectivity $R\left(\omega ,T\right)/R\left(\omega ,T=35\text{K}\right)$, (b) optical conductivity ${\sigma }_1\left(\omega ,T\right)/{\sigma }_1\left(\omega ,T=35\text{K}\right)$, and (c) frequency-dependent optical scattering rate ${\tau }^{-1}\left(\omega ,T\right)/{\tau }^{-1}\left(\omega ,T=35\text{K}\right)$.