Superconducting gap structure in ambient-pressure-grown ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$

We have performed transverse-field muon spin relaxation measurements on ambient-pressure-grown polycrystalline $\mathrm{La}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$. From these measurements, no signature of magnetic order is found down to 25 mK. The value of the magnetic penetration depth extrapolated to 0 K is 0.89 (5) $\mu \mathrm{m}$. The temperature dependence of superconducting penetration depth is best described by either a multigap $s+s$-wave model with ${\mathrm{\Delta }}_1=0.947 \left(7\right) \mathrm{meV}$ and ${\mathrm{\Delta }}_2=0.22$ (4) meV or the anisotropic $s$-wave model with $\mathrm{\Delta }\left(0\right)=0.776 \mathrm{meV}$ and anisotropic gap amplitude ratio ${\mathrm{\Delta }}_{\text{min}}/{\mathrm{\Delta }}_{\text{max}}=0.34$. Comparisons with other potentially multigap ${\mathrm{BiS}}_2$-based superconductors are discussed. We find that these ${\mathrm{BiS}}_2$-based superconductors, including ${\mathrm{Bi}}_4{\mathrm{O}}_4{\mathrm{S}}_3$ and the high-pressure synthesized $\mathrm{La}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$, generally conform to the Uemura relation.

Figure 1

TF-$\mu \mathrm{SR}$ spectra from $\mathrm{La}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ (AP) in the normal (circles) and superconducting (squares) states with an external magnetic field of $H_{\text{ext}}=266 \mathrm{Oe}$. Solid curves are fits to the raw data with Eq. (1). For clarity, the spectra are shown in a rotating reference frame corresponding to a field of 220 Oe [30].

Figure 2

(a) Temperature dependence of exponential muon relaxation rate $\mathrm{\Lambda }$ in $\mathrm{La}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ (AP). For all temperatures measured $\mathrm{\Lambda }$ displays little temperature dependence. (b) The Gaussian relaxation rate $\sigma$ as a function of temperature. The arrow represents the $T_c$ determined from specific heat [2]. The dashed dark brown curve is the fit to Eq. (2). Open circles and diamonds represent data taken from the DR and the LAMPF spectrometers, respectively.

Figure 3

Penetration depth plotted as ${\lambda }^{-2}\left(T\right)/{\lambda }^{-2}\left(0\right)$ vs reduced temperature $T/T_c$ for $\mathrm{La}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$. Curves correspond to the two-gap $s+s$-wave model (solid line), single gap BCS $s$-wave model (dash-dotted line), anisotropic $s$-wave model (dash-dot-dotted line), as well as a power-law fit (dashed line). Solid black lines labeled with $s$-wave 1 and $s$-wave 2 represent the individual contributions from the two $s$-wave gaps in the $s+s$-wave model. The inset shows ${\lambda }^{-2}\left(T\right)$/${\lambda }^{-2}\left(0\right)$ vs $\log T/T_c$ (K), highlighting the quality of fit in the low-temperature regime. Data points taken at the DR and the LAMPF spectrometers are represented by the circle and diamond symbols.

Figure 4

The correlations between $T_c$ and ${\lambda }_{ab}^{-2}$ (proportional to the superfluid density $n_s/m^{*}$) of the polycrystalline ${\mathrm{BiS}}_2$-based superconductors ${\mathrm{Bi}}_4{\mathrm{O}}_4{\mathrm{S}}_3$ [14], $\mathrm{La}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ (AP), and $\mathrm{La}{\mathrm{O}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$(HP) [11]. Inset: Uemura plot of the hole-doped iron-based superconductors (diamonds) and high-$T_c$ cuprates (squares) as well as the ${\mathrm{BiS}}_2$-based superconductors (circles).