Title: Anisotropic two-gap superconductivity and the absence of a Pauli paramagnetic limit in single-crystalline LaO$_{0.5}$F$_{0.5}$BiS$_2$,
Abstract: Ambient-pressure-grown LaO$_{0.5}$F$_{0.5}$BiS$_2$ with a superconducting
transition temperature $T_{c}\sim$3K 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 the first datasets displaying the temperature dependence of the
out-of-plane upper critical field $H_{c2}^{\perp}(T)$, the in-plane upper
critical field $H_{c2}^{\parallel}(T)$, as well as the angular dependence of
$H_{c2}$ at fixed temperatures for ambient-pressure-grown
LaO$_{0.5}$F$_{0.5}$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 $H_{c2}^{\parallel}(T)$ is observed near $T_{c}$, which we
analyze using a two-gap model. Moreover, $H_{c2}^{\parallel}(0)$ 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 BiS$_2$ bilayers. Hence,
LaO$_{0.5}$F$_{0.5}$BiS$_2$ with a centrosymmetric lattice structure is a
unique platform to explore the physics associated with local parity violation
in the bulk crystal.