Upper critical field of \textit{Ln}O$_{\mathrm{0.5}}$F$_{\mathrm{0.5}}$BiS$_{\mathrm{2}}$ (\textit{Ln} $=$ La, Nd) superconductors at extreme conditions

One of the most interesting phenomena displayed by many BiS2-based superconductors including \textit{Ln}O$_{\mathrm{1-}}_{x}$F$_{x}$BiS$_{\mathrm{2}}$ (\textit{Ln} $=$ La-Nd) is the rather abrupt enhancement of superconducting transition temperature ($T_{c})$ under high pressure (HP). In this study, we investigated the upper critical field $H_{c}_{\mathrm{2\thinspace }}$of polycrystalline samples of \textit{Ln}O$_{\mathrm{0.5}}$F$_{\mathrm{0.5}}$BiS$_{\mathrm{2}}$ (\textit{Ln} $=$ La, Nd) at ambient pressure and high pressure at various magnetic fields up to 8.5 T. For the LaO$_{\mathrm{0.5}}$F$_{\mathrm{0.5}}$BiS$_{\mathrm{2}}$ sample under HP $H_{c}_{\mathrm{2}}$ shows an anomalous behavior between 5 and 6 T. However, such anomalous behavior is very subtle for NdO$_{\mathrm{0.5}}$F$_{\mathrm{0.5}}$BiS$_{\mathrm{2}}$ under HP. The results explain why the pressure-induced enhancement of $T_{c}$ for NdO$_{\mathrm{0.5}}$F$_{\mathrm{0.5}}$BiS$_{\mathrm{2}}$ is not as large as that for LaO$_{\mathrm{0.5}}$F$_{\mathrm{0.5}}$BiS$_{\mathrm{2}}$ and also support the idea that local atomic environment, is possibly more essential to the enhancement of $T_{c}$ for BiS$_{\mathrm{2}}$-based superconductors than the structural phase transition.