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Cho et al. [Phys. Rev. B, 84, 174502 (2011)] have reported on the temperature dependence of the London penetration depth deduced from Tunnel Diode Oscillator (TDO) measurements in optimally doped Fe(Se,Te) single crystals. According to their analysis, these measurements chould suggest a nodeless two-gap pairing symmetry with strong pair breaking effects. However, to reach this conclusion, the authors fit the temperature dependence of the superfluid density with a two band {it clean} limit model which is incompatible with the presence of strong pair breaking effects, deduced from the $T^n$ temperature dependence of the London penetration depth below $T_c/3$. Moreover they claim that their results are also ruling out the suggestion that surface conditions can significantly affect the TDO data but this conclusion is based on one very specific damaging process, and is completely ignoring the large dispersion in the previously published TDO data.
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The London penetration depth $lambda$ is the basic length scale for electromagnetic behavior in a superconductor. Precise measurements of $lambda$ as a function of temperature, field, and impurity scattering have been instrumental in revealing the nature of the order parameter and pairing interactions in a variety of superconductors discovered over the past decades. Here we recount our development of the tunnel-diode resonator technique to measure $lambda$ as a function of temperature and field in small single crystal samples. We discuss the principles and applications of this technique to study unconventional superconductivity in the copper oxides and other materials such as iron-based superconductors. The technique has now been employed by several groups worldwide as a precision measurement tool for the exploration of new superconductors.
We report combined experimental and theoretical analysis of superconductivity in CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ (CaK1144) for $x=$0, 0.017 and 0.034. To obtain the superfluid density, $rho=left(1+Delta lambda_L(T)/lambda_L(0) right)^{-2}$, the temperature dependence of the London penetration depth, $Delta lambda_L (T)$, was measured by using tunnel-diode resonator (TDR) and the results agreed with the microwave coplanar resonator (MWR) with the small differences accounted for by considering a three orders of magnitude higher frequency of MWR. The absolute value of $lambda_L (T ll T_c) approx lambda_L(0)$ was measured by using MWR, $lambda_L (mathrm{5~K}) approx 170 pm 20$ nm, which agreed well with the NV-centers in diamond optical magnetometry that gave $lambda_L (mathrm{5~K}) approx 196 pm 12$ nm. The experimental results are analyzed within the Eliashberg theory, showing that the superconductivity of CaK1144 is well described by the nodeless s$_{pm}$ order parameter and that upon Ni doping the interband interaction increases.
We show on a few examples of one-band materials with spheroidal Fermi surfaces and anisotropic order parameters that anisotropies $gamma_H$ of the upper critical field and $gamma_lambda$ of the London penetration depth depend on temperature, the feature commonly attributed to multi-band superconductors. The parameters $gamma_H$ and $gamma_lambda$ may have opposite temperature dependencies or may change in the same direction depending on Fermi surface shape and on character of the gap nodes. For two-band systems, the behavior of anisotropies is affected by the ratios of bands densities of states, Fermi velocities, anisotropies, and order parameters. We investigate in detail the conditions determining the directions of temperature dependences of the two anisotropy factors.
The London penetration depth, $lambda(T)$, has been measured in several single crystals of Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$. Thermodynamic, electromagnetic, and structural characterization measurements confirm that these crystals are of excellent quality. The observed low temperature variation of $lambda(T)$ follows a power-law, $Delta lambda (T) sim T^n$ with $n=2.4 pm 0.1$, indicating the existence of normal quasiparticles down to at least $0.02T_c$. This is in contrast to recent penetration depth measurements on single crystals of NdFeAsO$_{1-x}$F$_x$ and SmFeAsO$_{1-x}$F$_x$, which indicate an anisotropic but nodeless gap. We propose that a more three-dimensional character in the electronic structure of Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$ may lead to an anisotropic $s-$wave gap with point nodes that would explain the observed $lambda(T)$.
We study the effects of anisotropic order parameters on the temperature dependence of London penetration depth anisotropy $gamma_lambda(T)$. After MgB$_2$, this dependence is commonly attributed to distinct gaps on multi-band Fermi surfaces in superconductors. We have found, however, that the anisotropy parameter may depend on temperature also in one-band materials with anisotropic order parameters $Delta(T,k_F)$, a few such examples are given. We have found also that for different order parameters, the temperature dependence of $Delta(T)/Delta(0)$ can be represented with good accuracy by the interpolation suggested by D. Einzel, J. Low Temp. Phys, {bf 131}, 1 (2003), which simplifies considerably the evaluation of $gamma_lambda(T)$. Of particular interest is mixed order parameters of two symmetries for which $gamma_lambda(T)$ may go through a maximum for a certain relative weight of two phases. Also, for this case, we find that the ratio $Delta_{max}(0)/T_c$ may exceed substantially the weak coupling limit of 1.76. It, however, does not imply a strong coupling, rather it is due to significantly anisotropic angular variation of $Delta$.
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