Evolution of London penetration depth with scattering in single crystals of K$_{1-x}$Na$_x$Fe$_2$As$_2$

TL;DR

This study investigates how impurity scattering affects the London penetration depth in K$_{1-x}$Na$_x$Fe$_2$As$_2$ single crystals, revealing a transition from linear to quadratic temperature dependence and supporting a d-wave pairing symmetry.

Contribution

It demonstrates that impurity scattering induces a transition from linear to quadratic temperature dependence of the penetration depth, supporting a simple d-wave superfluid density model.

Findings

Impurity substitution increases scattering and suppresses $T_c$.

The temperature dependence of $ riangle \lambda(T)$ shifts from linear to quadratic with impurities.

Superfluid density follows a d-wave dependence, contradicting multi-band gap scenarios.

Abstract

London penetration depth, $\lambda (T)$, was measured in single crystals of K$_{1-x}$Na$_x$Fe$_2$As$_2$, $x$=0 and 0.07, down to temperatures of 50~mK, $\sim T_c/50$. Isovalent substitution of Na for K significantly increases impurity scattering, with $\rho(T_c)$ rising from 0.2 to 2.2 $\mu \Omega$cm, and leads to a suppression of $T_c$ from 3.5~K to 2.8~K. At the same time, a close to $T$-linear $\Delta \lambda (T)$ in pure samples changes to almost $T^2$ in the substituted samples. The behavior never becomes exponential as expected for the accidental nodes, as opposed to $T^2$ dependence in superconductors with symmetry imposed line nodes. The superfluid density in the full temperature range follows a simple clean and dirty $d$-wave dependence, for pure and substituted samples, respectively. This result contradicts suggestions of multi-band scenarios with strongly different gap structure on four sheets of the Fermi surface.