Linear-brush diblock copolymers bearing carbazole moieties in the brush block were synthesized. Various phase-separated nanostructures were found to develop in nanoscale thin films of the copolymers, depending on the fabrication conditions including selective solvent-annealing. This variety of morphologies and orientations means that these block copolymers exhibit digital memory versatility in their devices. Overall, the relationship between the morphology and digital memory performance of these copolymers has several important features. In particular, the carbazole moieties in the vertical cylinder phase with a radius of 8 nm or less can trap charges and also form local hopping paths for charge transport, which opens the mass production of advanced digital memory devices with ultrahigh memory density. Charges can be transported through the layer when the dielectric linear block phase has a thickness of 10.6 nm; however, charge transport is not possible for a dielectric phase with a thickness of 15.9 nm. All the observed memory behaviors are governed by the trap-limited space-charge-limited conduction mechanism and local hopping path (i.e., filament) formation.