Competition between superconductivity and magnetic/nematic order as a source of anisotropic superconducting gap in underdoped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$

Abstract

The in-plane London penetration depth, $\hat{I}”\hat{I}»(T)$, was measured using a tunnel diode resonator technique in single crystals of Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ with doping levels $x$ ranging from heavily underdoped, $x$=0.16 ($T_c$=7~K) to nearly optimally doped, $x$= 0.34 ($T_c=$39 K). Exponential saturation of $\hat{I}”\hat{I}»(T)$ in the $T\to 0$ limit is found in optimally doped samples, with the superfluid density $\ddot{I}{}_s(T)\equiv (\hat{I}»(0)/\hat{I}»(T){)}^2$ quantitatively described by a self-consistent ${\hat{I}}^3$-model with two nodeless isotropic superconducting gaps. As the doping level is decreased towards the extreme end of the superconducting dome at $x$=0.16, the low-temperature behavior of $\hat{I}”\hat{I}»(T)$ becomes non-exponential and best described by the power-law $\hat{I}”\hat{I}»(T)\propto T^2$, characteristic of strongly anisotropic gaps. The change between the two regimes happens within the range of coexisting magnetic/nematic order and superconductivity, $x<0.25$, and is accompanied by a rapid rise in the absolute value of $\hat{I}”\hat{I}»(T)$ with underdoping. This effect, characteristic of the competition between superconductivity and other ordered states, is very similar to but of significantly smaller magnitude than what is observed in the electron-doped Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ compounds. Our study suggests that the competition between superconductivity and magnetic/nematic order in hole-doped compounds is weaker than in electron-doped compounds, and that the anisotropy of the superconducting state in the underdoped iron pnictides is a consequence of the anisotropic changes in the pairing interaction and in the gap function promoted by both magnetic and nematic long-range order.