Doping dependence of the critical fluctuation regime in the Fe-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$

TL;DR

This study examines how superconducting fluctuations vary with doping in Ba$_{1-x}$K$_x$Fe$_2$As$_2$, revealing a doping-dependent fluctuation regime influenced by magnetic field effects across the phase diagram.

Contribution

It provides the first detailed analysis of doping-dependent fluctuation regimes in Fe-based superconductors using high-resolution thermodynamic measurements and fluctuation models.

Findings

Fluctuation regimes are strongest in underdoped and overdoped samples.

Magnetic field induces a finite size effect reducing effective dimensionality.

Transition broadening correlates with increased critical fluctuations at certain dopings.

Abstract

We investigate the importance of superconducting order parameter fluctuations in the 122 family of Fe-based superconductors, using high-resolution specific heat and thermal expansion data of various Ba$_{1-x}$K$_x$Fe$_2$As$_2$ single crystals covering a large range of the phase diagram from the strongly underdoped to the overdoped regime. By applying scaling relations of the 3d-XY and the 3d-Lowest-Landau-Level (3d-LLL) fluctuation models to data measured in different magnetic fields, we demonstrate that a strong increase of the critical fluctuation regime is responsible for the transition broadening in magnetic fields, which is a direct consequence of a magnetic-field-induced finite size effect due to a reduction of the effective dimensionality by a decreasing magnetic length scale related to the mean vortex separation and the confinement of quasiparticles in low Landau levels. The fluctuations are stronger in the underdoped and overdoped regimes and appear to be weakest at optimal doping.