# Band-selective clean- and dirty-limit superconductivity with nodeless gaps in the bilayer iron-based superconductor CsCa$_2$Fe$_4$As$_4$F$_2$

## TL;DR

This study reveals band-selective coexistence of clean- and dirty-limit nodeless superconductivity in CsCa$_2$Fe$_4$As$_4$F$_2$, characterized by distinct optical responses and gap features in different electronic bands.

## Contribution

It provides the first optical evidence of band-selective clean- and dirty-limit superconductivity with nodeless gaps in a bilayer iron-based superconductor.

## Key findings

- Observation of a nodeless superconducting gap below 110 cm$^{-1}$
- Identification of a dirty-limit gap with 2Δ ≈ 14 meV in the broad Drude component
- Detection of a clean-limit response with spectral weight transferred to the condensate

## Abstract

The optical properties of the new iron-based superconductor CsCa$_2$Fe$_4$As$_4$F$_2$ with $T_c \sim 29$~K have been determined. In the normal state a good description of the low-frequency response is obtained with a superposition of two Drude components of which one has a very low scattering rate (narrow Drude-peak) and the other a rather large one (broad Drude-peak). Well below $T_c \sim 29$~K, a pronounced gap feature is observed which involves a complete suppression of the optical conductivity below $\sim$ 110~cm$^{-1}$ and thus is characteristic of a nodeless superconducting state. The optical response of the broad Drude-component can be described with a dirty-limit Mattis-Bardeen-type response with a single isotropic gap of $2\Delta \simeq 14$~meV. To the contrary, the response of the narrow Drude-component is in the ultra-clean-limit and its entire spectral weight is transferred to the zero-frequency $\delta(\omega)$ function that accounts for the loss-free response of the condensate. These observations provide clear evidence for a band-selective coexistence of clean- and dirty-limit superconductivity with nodeless gaps in CsCa$_2$Fe$_4$As$_4$F$_2$.