Strong-Coupling Superconductivity in NaFe$_{1-x}$Co$_x$As: the Eliashberg Theory and Beyond

TL;DR

This study investigates the superconducting and normal-state properties of NaFe$_{1-x}$Co$_x$As using specific heat measurements, revealing strong suppression of certain parameters and suggesting modifications to existing boson-exchange models for high-$T_c$ superconductivity.

Contribution

It provides experimental insights into the superconducting gap structure and challenges the applicability of standard Eliashberg theory to this system, indicating the need for model modifications.

Findings

Normal-state Sommerfeld coefficient is suppressed in underdoped and overdoped samples.

Superconducting specific heat fits both one-gap and two-gap BCS models.

The ratio $rac{ riangle C}{T_c imes ext{Sommerfeld coefficient}}$ exceeds model predictions near optimal doping.

Abstract

We study the normal-state and superconducting properties of NaFe$_{1-x}$Co$_x$As system by specific heat measurements. Both the normal-state Sommerfeld coefficient and superconducting condensation energy are strongly suppressed in the underdoped and heavily overdoped samples. The low-temperature electronic specific heat can be well fitted by either an one-gap or a two-gap BCS-type function for all the superconducting samples. The ratio $\gamma_NT_c^2/H_c^2(0)$ can nicely associate the neutron spin resonance as the bosons in the standard Eliashberg model. However, the value of $\Delta C/T_c\gamma_N$ near optimal doping is larger than the maximum value the model can obtain. Our results suggest that the high-$T_c$ superconductivity in the Fe-based superconductors may be understood within the framework of boson-exchange mechanism but significant modification may be needed to account for the finite-temperature properties.