BCS-like superconductivity in NdO${}_{1-x}$F${}_x$BiS${}_2$ ($x$ = 0.3 and 0.5) single crystals

We measure the magnetic penetration depth $\mathrm{\Delta }\lambda (T)$ for NdO${}_{1-x}$F${}_x$BiS${}_2$ ($x$ = 0.3 and 0.5) using the tunnel diode oscillator technique. The $\mathrm{\Delta }\lambda (T)$ shows an upturn in the low-temperature limit which is attributed to the paramagnetism of Nd ions. After subtracting the paramagnetic contributions, the penetration depth $\mathrm{\Delta }\lambda (T)$ follows exponential-type temperature dependence at $T\ll T_c$\mathrm{.}Both$\Delta\lambda(T)$andthecorrespondingsuperfluiddensity$\rho_s(T)$canbedescribedbytheBCSmodelwithanenergygapof$\Delta(0)$ $\approx$ 2.0 $k_B{T}_c$ for both $x$ = 0.3 and 0.5, suggesting strong-coupling BCS superconductivity in the presence of localized moments for NdO${}_{1-x}$F${}_x$BiS${}_2$.