High-$T_c$ superconductivity in ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ in absence of nematic fluctuations

We employ polarization-resolved Raman spectroscopy to study the multiband stoichiometric $T_c=35$ K superconductor ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$. We do not detect Pomeranchuk-like electronic nematic fluctuations which were universally observed in the $XY\left(B_{2g}\right)$ symmetry Raman response for most families of the Fe-based superconductors. In the superconducting state we observe, consistent with a nodeless order parameter, a full spectral weight suppression at low energies and the emergence of a composite pair-breaking coherence feature at energies between 12 and 20 meV. We analyze the superconductivity-induced phonon self-energy effects and give an estimation for the electron-phonon coupling constant ${\lambda }^{\mathrm{\Gamma }}=0.0015$ which is insufficient to provide attraction for high-$T_c$ pairing.

Figure 1

(a) The comparison between ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ and ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ lattice structures. For ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$, the Fe sites are shifted away from the high-symmetry $z=1/4$ and 3/4 planes, causing two distinct As-Fe bond distances (shown in blue and orange). (b) The reduction of the Fe site symmetry from $D_{2d}$ for ${\mathrm{CaFe}}_2{\mathrm{As}}_2$ to $C_{2v}$ for ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$. (c) For ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$, a sketch of the partially occupied $d_{xz}/d_{yz}$ orbital order (the upper panel for real space), and derived two FS pockets in the vicinity of the $\mathrm{\Gamma }$ point (the lower panel for momentum space). Solid and dotted lines denote differences in the orbital occupation which induce a static quadrupole moment on the Fe sites with a checkerboard order.

Figure 2

Raman spectra for single-crystal ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ at 40 and 7 K. The $XY$ and $XX$ polarized spectra are offset by 1 and 2 units, respectively. Inset: Top view of the Fe-As layer and axis notations.

Figure 3

Temperature evolution of the Raman response in the $B_{2g}$ channel. Error bars show one standard deviation. Red lines denote a model fit with three isotropic gap functions [15, 43]. Another model fit comprising an isotropic gap and a shallow collective mode is shown in blue. The decompositions are shown by dotted lines, where shadings denote one standard deviation error.

Figure 4

Temperature evolution of phonon spectra. (a) The $B_{1g}$ phonon spectra and the fitting curve for above (40 K) and below (7 K) $T_c$. Inset of (a): Atomic displacements of the $B_{1g}$ phonon. (b), (c) Temperature dependence of $B_{1g}$ phonon energy ${\omega }_{\text{ph}}$ and linewidth $2{\mathrm{\Sigma }}^{\prime \prime }$. ${\mathrm{\Sigma }}^{\prime \prime }$ has been corrected for the spectrometer resolution as shown in (a). Dashed lines describe the anharmonic decay into two phonons obtained from the fit for the normal state. (d), (e) The $A_{1g}\left(1\right)$ and $A_{1g}\left(3\right)$ phonon modes at 40 and 7 K.