Anisotropic two-gap superconductivity and the absence of a Pauli paramagnetic limit in single-crystalline ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$

Ambient-pressure-grown ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ with a superconducting transition temperature $T_c\sim 3$ K possesses a highly anisotropic normal state. By a series of electrical resistivity measurements with a magnetic-field direction varying between the crystalline $c$ axis and the $ab$ plane, we present datasets displaying the temperature dependence of the out-of-plane upper critical field $H_{c2}^{\perp }\left(T\right)$, the in-plane upper critical field $H_{c2}^{\parallel }\left(T\right)$, as well as the angular dependence of $H_{c2}$ at fixed temperatures for ambient-pressure-grown ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ single crystals. The anisotropy of the superconductivity, $H_{c2}^{\parallel }/H_{c2}^{\perp }$, reaches $\sim 16$ on approaching 0 K, but it decreases significantly near $T_c$. A pronounced upward curvature of $H_{c2}^{\parallel }\left(T\right)$ is observed near $T_c$, which we analyze using a two-gap model. Moreover, $H_{c2}^{\parallel }\left(0\right)$ is found to exceed the Pauli paramagnetic limit, which can be understood by considering the strong spin-orbit coupling associated with Bi as well as the breaking of the local inversion symmetry at the electronically active ${\mathrm{BiS}}_2$ bilayers. Hence, ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ with a centrosymmetric lattice structure is a unique platform to explore the physics associated with local parity violation in the bulk crystal.

Figure 1

Temperature dependence of resistivity $\rho \left(T\right)$ at ambient pressure without a magnetic field for crystal 1. Top inset: the enlarged resistivity curve near the superconducting transition, with the arrow indicating the $T_c$, defined as 50% of the normal state resistivity ${\rho }_n$. Bottom inset: the crystal structure of ${\mathrm{LaO}}_{0.5}{\mathrm{F}}_{0.5}{\mathrm{BiS}}_2$ with a space group of $P4/nmm$.

Figure 2

Temperature dependence of resistivity $\rho \left(T\right)$ for crystal 1 under various magnetic fields with (a) $H\perp ab$ and (b) $H\parallel ab$. Field dependence of resistivity $\rho \left(H\right)$ at different temperatures with (c) $H\perp ab$ and (d) $H\parallel ab$. The black arrow indicates increasing temperatures. Representative curves covering a longer field range are labeled in the legend.

Figure 3

Temperature dependence of $H_{c2}$ with $H\parallel ab$ and $H\perp ab$ for crystal 1. Experimental data, shown in symbols, are fitted with the two-gap model (dashed line) and the Werthamer-Helfand-Hohenberg (WHH) theory (dash-dotted line). Inset: the enlargement of the low-field region for a clearer view of $H_{c2}^{\perp }\left(T\right)$.

Figure 4

Angular dependence of $H_{c2}$ for crystal 2 at 2, 2.3, and 2.55 K (solid symbols). The solid lines are the fits using the two-gap model. The angle $\theta ={90}^{\circ }\left(0^{\circ }\right)$ corresponds to $H\parallel ab\left(H\perp ab\right)$. Top inset: $H\text{−}T$ phase diagram constructed for crystal 2, showing a temperature dependence similar to the sample discussed earlier. Arrows indicate the temperatures where angular-dependent studies were conducted. Bottom inset: expanded low-field region for a clearer view of $H_{c2}\left(\theta \right)$ at 2.55 K.