Self-consistent two-gap approach in studying multi-band superconductivity in NdFeAsO${}_{0.65}$F${}_{0.35}$

Abstract

High-quality single crystals of NdFeAsO${}_{0.65}$F${}_{0.35}$ (the transition temperature $T_{\mathrm{c}}\simeq 30.6$~K) were studied in zero-field (ZF) and transverse-field (TF) muon-spin rotation/relaxation ($\mu$SR) experiments. An upturn in muon-spin depolarization rate at $T\lesssim 3$~K was observed in ZF-$\mu$SR measurements and it was associated with the onset of ordering of Nd electronic moments. Measurements of the magnetic field penetration depth ($\lambda$) were performed in the TF geometry. By applying the external magnetic field $B_{\mathrm{ex}}$ parallel to the crystallographic $c$-axis ($B_{\mathrm{ex}}\Vert c$) and parallel to the $ab$-plane ($B_{\mathrm{ex}}\Vert ab$), the temperature dependencies of the in-plane component (${\lambda }_{ab}^{-2}$) and the combination of the in-plane and the out of plane components (${\lambda }_{ab,c}^{-2}$) of the superfluid density were determined, respectively. The out-of-plane superfluid density component (${\lambda }_c^{-2}$) was further obtained by combining the results of $B_{\mathrm{ex}}\Vert c$ and $B_{\mathrm{ex}}\Vert ab$ set of experiments. The temperature dependencies of ${\lambda }_{ab}^{-2}$, ${\lambda }_{ab,c}^{-2}$, and ${\lambda }_c^{-2}$ were analyzed within the framework of a self-consistent two-gap model despite of using the traditional $\alpha$-model. Interband coupling was taken into account, instead of assuming it to be zero as it stated in the $\alpha$-model. A relatively small value of the interband coupling constant ${\Lambda }_{12}\simeq 0.01$ was obtained, thus indicating that the energy bands in NdFeAsO${}_{0.65}$F${}_{0.35}$ are only weakly coupled. In spite of their small magnitude, the coupling between the bands leads to the single value of the superconducting transition temperature $T_{\mathrm{c}}$.

arXiv comment10 pages, 8 figures

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