c-axis magnetotransport and noise in underdoped La$_{2-x}$Sr$_x$CuO$_4$

We report a study of c-axis magnetotransport and noise on high quality single crystals of La$_{2-x}$Sr$_x$CuO$_4$ ($x=0.03$). The measurements were performed at temperatures 0.110$\leq T$(K) $\leq 50$ and fields $0\leq B$(T)$\leq 18$ parallel and perpendicular to the c axis. Our experiments have revealed for the first time a number of glassy features in the charge response at very low $T$, such as memory effects and history dependence. In the same $T$ range, we have observed positive magnetoresistance (MR), which exhibits hysteretic behavior. The hysteretic effects decrease with increasing $T$ and vanish at $\sim1.5$~K. The crossover from positive to negative MR takes place at higher $T$ and $B$. We have also observed switching fluctuations in the time-dependent resistance at the lowest $T$, with switching times varying from several minutes to several hours. The possible origins of the observed glassiness will be discussed.