Electrical resistivity measurements have been performed on the iron-based ladder compounds Ba$_{1-x}$Cs$_x$Fe$_2$Se$_3$ ($x$ = 0, 0.25, 0.65, and 1) under high pressure. A cubic anvil press was used up to 8.0 GPa, whereas further higher pressure was applied using a diamond anvil cell up to 30.0 GPa. Metallic behavior of the electrical conductivity was confirmed in the $x$ = 0.25 and 0.65 samples for pressures greater than 11.3 and 14.4 GPa, respectively, with the low-temperature $log T$ upturn being consistent with weak localization of 2D electrons due to random potential. At pressures higher than 23.8 GPa, three-dimensional Fermi-liquid-like behavior was observed in the latter sample. No metallic conductivity was observed in the parent compounds BaFe$_2$Se$_3$ ($x $ = 0) up to 30.0 GPa and CsFe$_2$Se$_3$ ($x$ = 1) up to 17.0 GPa. The present results indicate that the origins of the insulating ground states in the parent and intermediate compounds are intrinsically different; the former is a Mott insulator, whereas the latter is an Anderson insulator owing to the random substitution of Cs for Ba.
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