Optical signature of subgap absorption in the superconducting state of $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$

The optical conductivity of $\text{Ba}{\left({\text{Fe}}_{0.92}{\text{Co}}_{0.08}\right)}_2{\text{As}}_2$ shows a clear signature of the superconducting gap but a simple $s$-wave description fails in accounting for the low-frequency response. This task is achieved by introducing an extra Drude peak in the superconducting state representing subgap absorption, other than thermally broken pairs. This extra peak and the coexisting $s$-wave response respect the total sum rule indicating a common origin for the carriers. We discuss the possible origins for this absorption as (i) quasiparticles due to pair breaking from interband impurity scattering in a two-band $s_{\pm }$-gap symmetry model, which includes (ii) the possible existence of impurity levels within an isotropic gap model; or (iii) an indication that one of the bands is highly anisotropic.

Figure 1

(Color online) Reflectivity of $\text{Ba}{\left(\text{Fe},\text{Co}\right)}_2{\text{As}}_2$ at low temperatures above and below $T_c=22.5\text{K}$. The inset shows the 300 K reflectivity in the full measured spectral range.

Figure 2

(Color online) The open circles are the real part of the optical conductivity at 15 K and the open triangles at 30 K. The solid lines going through these points are fits to the data using Eq. (1). In the normal state the fit is composed of a Drude term $\left({\Omega }_p=9250{\text{cm}}^{-1};{\tau }^{-1}=210{\text{cm}}^{-1}\right)$ and a Lorentz peak $\left(\Omega =114{\text{cm}}^{-1};S=2071{\text{cm}}^{-1};\gamma =61{\text{cm}}^{-1}\right)$. In the superconducting state, the same Lorentz peak is kept and the Drude term has its spectral weight divided up between a Mattis-Bardeen $s$-wave gap $\left({\Omega }_p^N=8210{\text{cm}}^{-1};{\tau }_N^{-1}=200{\text{cm}}^{-1};2\Delta =50{\text{cm}}^{-1}\right)$ and a residual Drude peak $\left({\Omega }_p=4450{\text{cm}}^{-1};{\tau }^{-1}=53{\text{cm}}^{-1}\right)$.

Figure 3

(Color online) The top panel shows the measured ${\sigma }_1$ (symbols) at various temperatures and corresponding fits (solid lines) using Eq. (1). The symbols in the bottom panel are the measured superconducting-to-normal reflectivity ratios $\left(R_S/R_N\right)$ and the simulations obtained by using the parameters that fit the optical conductivity. $R_N$ is taken at 25 K. The blue dashed line is the best fit assuming that the superconducting state has no unpaired quasiparticles due to scattering pair breaking (no Drude term).

Figure 4

(Color online) The symbols in the left panel depict the temperature evolution of the penetration depth calculated from the imaginary part of the optical conductivity. The solid line is a single gap BCS calculation with $2\Delta =50{\text{cm}}^{-1}$. The dashed line is a quadratic $\left(\Delta \lambda =3.2T^2\right)$ behavior. The right panel shows the application of the $f$-sum rule to $\text{Ba}{\left(\text{Fe},\text{Co}\right)}_2{\text{As}}_2$. The solid blue circles are the spectral weight of the Drude term in both normal and superconducting states. The solid triangles represent the total weight in the superconducting state, including the superfluid stiffness.