How robust the global measurements of London penetration depth are: the case of Fe(Te$_{1-x}$,Se$_{x}$)

Abstract

We report tunnel diode resonator measurements of in-plane London penetration depth, $\lambda(T)$, in optimally-doped single crystals of Fe(Te$_{0.58}$Se$_{0.42}$) with $T_c\sim$ 14.8 K. Systematic measurements were carried out for six samples with different size and surface roughness. The power-law behavior, $\Delta \lambda(T) = A T^n$ was found for all samples with the average exponent $n_{avg} = 2.3 \pm 0.1$ and the pre-factor $A_{avg} = 1.0 \pm 0.2$ nm/K$^{2.3}$. The average superfluid density is well described by the self-consistent two-gap $\gamma$ model resulting in $\Delta_{_{I}}(0)/k_B T_c$ = 1.93 and $\Delta_{_{II}}(0)/k_B T_c$ = 0.9. By analyzing the data obtained on samples of different size and deliberately introduced surface roughness, it is concluded that the calibration procedure used to obtain $\lambda(T)$ from the measured TDR frequency shift is quite robust and the uncertainty in sample dimensions and the nature of surface roughness play only minor role. The exponent $n$, directly related to the superconducting gap structure, remains virtually unchanged. The calibration - dependent pre-factor $A$ shows some variation, but stays within reasonable margin ruling out some recent suggestions that surface conditions can significantly affect the results. Our results confirm that precision global measurements provide the most objective information regarding temperature - dependent London penetration depth.