Anomalous phonon behavior in superconducting ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$: An optical study

The temperature dependence of $ab$-plane optical conductivity of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ has been measured below and above its superconducting transition temperature $T_c\simeq 35.5$ K. In the normal state, analysis with the two-Drude model reveals a $T$-linear scattering rate for the coherent response, which suggests strong spin-fluctuation scattering. Below the superconducting transition, the optical conductivity below 120 ${\mathrm{cm}}^{-1}$ vanishes, indicating nodeless gap(s). The Mattis-Bardeen fitting in the superconducting state gives two gaps of ${\mathrm{\Delta }}_1\simeq 9$ meV and ${\mathrm{\Delta }}_2\simeq 14$ meV, in good agreement with recent angle-resolved photoemission spectroscopy (ARPES) results. In addition, around 255 ${\mathrm{cm}}^{-1}$, we observe two different infrared-active Fe-As modes with obvious asymmetric lineshape, originating from strong coupling between lattice vibrations and spin or charge excitations. Considering a moderate Hund's rule coupling determined from spectral weight analysis, we propose that the strong fluctuations induced by the coupling between itinerant carriers and local moments may affect the phonon mode, and the electron-phonon coupling through the spin channel is likely to play an important role in the unconventional pairing in iron-based superconductors.

Figure 1

Temperature dependence of resistivity of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$, the blue circles denote the zero-frequency extrapolation of its optical conductivity. The lower inset shows the magnetic susceptibility of the sample ($\chi$ represents the magnetic susceptibility per unit volume). Both of them show a sharp superconducting transition at $T_c=35.5$ K. The upper inset shows the lattice structure of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$; there are two different Fe-As bonds in one FeAs layer.

Figure 2

(a) Reflectivity (b) and optical conductivity of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ at various temperatures above and below the superconducting transition. The insets are the data in a larger energy area.

Figure 3

(a) Optical conductivity of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ at 150 K (thick black lines), fitted with the Drude-Lorentz model (thin red lines) and its decomposition into individual Drude and Lorentz terms. (b) The optical conductivity of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ in the SC state is fit using the Mattis-Bardeen formalism, which results in two SC gaps with the size of ${\mathrm{\Delta }}_1\simeq 9\pm 0.2$ meV and ${\mathrm{\Delta }}_2\simeq 14\pm 0.5$ meV. (c) The plasma frequency ${\mathrm{\Omega }}_p$ and (d) scattering rate $1/\tau$ for the narrow Drude (red); broad Drude (blue) components are extracted by fitting the data at various temperatures in the normal state.

Figure 4

(a) The real part of the optical conductivity of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ above and below $T_c\simeq 35.5$ K in the region of the infrared-active mode around 255 ${\mathrm{cm}}^{-1}$, from which we observe two different phonon modes. (b) The black squares denote the resonance frequency ${\omega }_0$ of the Fe-As mode at 295 K for ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ and ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$; the red circles denote the calculated frequency based on the Fe-As bond length. (c) The phonon modes in ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ (CKFA), ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ (CFA), and ${\mathrm{KFe}}_2{\mathrm{As}}_2$ (KFA) at 295 K, from which we observe the softening and enhancement of the phonon in ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$. (d) The fitting to the phonon modes in ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ at 50 K with a Fano and a Lorentz model, from which we observe a discrepancy for the Lorentz fit (indicated by the arrow), while the Fano model gives a better result.

Figure 5

The temperature dependence of the (a) infrared-active mode compared with the anharmonic decay model (dashed dotted line), (b) oscillator strength, (c) asymmetry parameter, and (d) linewidth.

Figure 6

Ratio of the integrated spectral weight SW(100 K)/SW(295 K), where $\mathrm{SW}={\int }_0^{{\omega }_c}{\sigma }_1\left(\omega \right)d\omega$, as a function of the cutoff frequency ${\omega }_c$, in ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ and ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$.