Superconductivity-induced transverse plasma mode and phonon anomaly in the $c$-axis response of the bilayer compound RbCa${}_2$Fe${}_4$As${}_4$F${}_2$

Abstract

With infrared spectroscopy we studied the out-of-plane ($c$-axis) response of the iron arsenide superconductor ACa${}_2$Fe${}_4$As${}_4$F${}_2$ (A = Rb,Cs) which has a bilayer structure similar to the high $T_c$ cuprates YBa${}_2$Cu${}_3$O${}_7$ (YBCO) and Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$ (Bi2212). In analogy to the cuprates, we observe a superconductivity-induced transverse plasma mode (tPM) and a phonon anomaly that are both signatures of local electric field effects that arise from a large difference between the local conductivities in the intra- and inter-bilayer regions. Using a multilayer model developed for the cuprates, we obtain a good description of the $c$-axis response and derive the local conductivities at $T\simeq T_c$ of $\ddot{I}{ƒ}_1^{\mathrm{bl}}(\ddot{I}‰\to 0)\simeq$ 1\,000 $\hat{I}{\text{c◯}}^{-1}{\mathrm{cm}}^{-1}$ and $\ddot{I}{ƒ}_1^{\mathrm{int}}(\ddot{I}‰\to 0)\simeq$ 15 $\hat{I}{\text{c◯}}^{-1}{\mathrm{cm}}^{-1}$, respectively, that are similar to the ones previously found in underdoped YBCO. Different from the cuprates, we find no evidence of a normal state pseudogap in terms of a partial suppression of the low-energy electronic states that sets in already well above $T_c$. There is also no clear sign of an onset of precursor superconducting pairing correlations well above $T_c\simeq$ 30~K. This highlights that the pseudogap and the precursor superconducting pairing well above $T_c$ are unique features of the cuprates with their strong electronic correlations and, for example, not just the result of a strongly anisotropic electronic response due to the layered crystal structure.

10 pages, 8 figures