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Ambient-pressure-grown LaO$_{0.5}$F$_{0.5}$BiS$_2$ with a superconductingtransition temperature $T_{c}\sim$3K possesses a highly anisotropic normalstate. By a series of electrical resistivity measurements with a magnetic fielddirection varying between the crystalline $c$-axis and the $ab$-plane, wepresent the first datasets displaying the temperature dependence of theout-of-plane upper critical field $H_{c2}^{\perp}(T)$, the in-plane uppercritical field $H_{c2}^{\parallel}(T)$, as well as the angular dependence of$H_{c2}$ at fixed temperatures for ambient-pressure-grownLaO$_{0.5}$F$_{0.5}$BiS$_2$ single crystals. The anisotropy of thesuperconductivity, $H_{c2}^{\parallel}/H_{c2}^{\perp}$, reaches $\sim$16 onapproaching 0 K, but it decreases significantly near $T_{c}$. A pronouncedupward curvature of $H_{c2}^{\parallel}(T)$ is observed near $T_{c}$, which weanalyze using a two-gap model. Moreover, $H_{c2}^{\parallel}(0)$ is found toexceed the Pauli paramagnetic limit, which can be understood by considering thestrong spin-orbit coupling associated with Bi as well as the breaking of thelocal inversion symmetry at the electronically active BiS$_2$ bilayers. Hence,LaO$_{0.5}$F$_{0.5}$BiS$_2$ with a centrosymmetric lattice structure is aunique platform to explore the physics associated with local parity violationin the bulk crystal.

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