Indication of subdominant $d$-wave interaction in superconducting ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$

We report inelastic light scattering results on the stoichiometric and fully ordered superconductor ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ as a function of temperature and light polarization. In the energy range between 10 and 315 ${\mathrm{cm}}^{-1}$ (1.24 and 39.1 meV) we observe the particle-hole continuum above and below the superconducting transition temperature $T_c$ and seven of the eight Raman active phonons. The main focus is placed on the analysis of the electronic excitations. Below $T_c$ all three symmetries projected with in-plane polarizations display a redistribution of spectral weight characteristic for superconductivity. The energies of the pair-breaking peaks in $A_{1g}$ and $B_{2g}$ symmetry are in approximate agreement with the results from photoemission studies. In $B_{1g}$ symmetry the difference between the normal and superconducting state is most pronounced, and the feature is shifted downwards with respect to those in $A_{1g}$ and $B_{2g}$ symmetry. The maximum peaking at 134 ${\mathrm{cm}}^{-1}$ (16.6 meV) has a substructure on the high-energy side. We interpret the peak at 134 ${\mathrm{cm}}^{-1}$ in terms of a collective Bardasis-Schrieffer (BS) mode and the substructure as a remainder of the pair-breaking feature on the electron bands. There is a very weak peak at 50 ${\mathrm{cm}}^{-1}$ (6.2 meV) which is tentatively assigned to another BS mode.

Figure 1

Structure and Fermi surface of ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$. (a) Tetragonal unit cell with the Ca, K, Fe, and As atoms shown in blue, gold, red, and green, respectively [1]. (b) Quasi-two-dimensional (2D) ${\mathrm{Fe}}_2{\mathrm{As}}_2$ layer with the solid orange line depicting the 1-Fe unit cell. (c) Brillouin zone of the 1-Fe cell. The three hole bands labeled $\alpha$, $\beta$, and $\gamma$ (blue) encircle the $\mathrm{\Gamma }$ point. The electron bands ${\delta }_1$ and ${\delta }_2$ (red) are centered at the $X$ and $Y$ points, respectively (adopted from Mou et al. [3]).

Figure 2

Raman response in ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ at symmetries and polarizations as indicated. Shown are raw data for $T\ll T_c$ (blue), $T>T_c$ (red), and difference spectra (orange). Phonon modes are present in the $A_{1g}$ and $B_{2g}$ spectra. (a) The pair-breaking maximum extends from ${\mathrm{\Omega }}_0^{(A_{1g})}=120\pm 5{\mathrm{cm}}^{-1}$ to ${\mathrm{\Omega }}_{\mathrm{m}}\approx 230{\mathrm{cm}}^{-1}$. The gap energies $2{\mathrm{\Delta }}_i$ for the four bands $i$ observed by ARPES [3] are reproduced as horizontal bars. Note that the right vertical axis is expanded by a factor of 2.5 with respect to the left one. (b) The $B_{1g}$ pair-breaking peak is well defined and sets on at ${\mathrm{\Omega }}_0^{(B_{1g})}=116\pm 5{\mathrm{cm}}^{-1}$. (c) The weak $B_{2g}$ pair-breaking peak is located slightly above $2{\mathrm{\Delta }}_{\beta }$. The intersection of the normal and superconducting spectra is close to ${\mathrm{\Omega }}_0^{(B_{2g})}=130\pm 5{\mathrm{cm}}^{-1}$.

Figure 3

Difference spectra of the $B_{1g}$ Raman response in ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ and ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ for temperatures as indicated. For raw data, cf. Fig. 2 and S5 of Ref. [14]. The main peak exhibits a double structure (orange and blue arrows). A second hump is visible in the spectra at 11, 13, and 17 K (asterisks) above the spectral shape expected for a clean gap (colored dashes). (f) Difference spectrum of ${\mathrm{Ba}}_{0.65}{\mathrm{K}}_{0.35}{\mathrm{As}}_2{\mathrm{Fe}}_2$. From Ref. [10]. The arrows show two Bardasis-Schrieffer modes at $3.1k_B{T}_c$ (green arrow) and $5.2k_B{T}_c$ (orange arrow). The remainder of the pair-breaking peak is located at $6.2k_B{T}_c$ (blue arrow) since the high-energy part is drained into the BS modes.