Highly anisotropic superconducting gap in underdoped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$

Abstract

The in-plane London penetration depth, $\Delta \lambda (T)$, was measured using a tunnel diode resonator in single crystals of Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ for five doping levels $x$ ranging from underdoped, $T_c$=11 K ($x$=0.17), to optimally doped, $T_c=$38 K ($x_{\text{opt}}$= 0.35). In the optimally doped samples, $\Delta \lambda (T)$ shows exponential saturation in $T\to 0$ limit suggesting a fully gapped superconductivity. The lowest-$T_c$ samples show much stronger non-exponential variation of $\Delta \lambda (T)$. Fitting the data to a power-law, $\Delta \lambda (T)=A{T}^n$, reveals a monotonic decrease of the exponent $n$ with $x$ towards the underdoped edge of the superconducting dome. Comparison with $n\approx 1.2$ reported in KFe${}_2$As${}_2$ ($T_c$=3.5 K, $x=$ 1), suggests a dome-like variation of $n$ with $x$, implying an evolution of the topology of the superconducting gap from full and isotropic in the center of the dome towards strongly anisotropic and, eventually, nodal at the dome edges.