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In this article we report on the experimental realization of dimensionalcrossover phenomena in the chain compound PrBa$_2$Cu$_4$O$_8$ usingtemperature, high magnetic fields and disorder as independent tuningparameters. In purer crystals of PrBa$_2$Cu$_4$O$_8$, a highly anisotropicthree-dimensional Fermi-liquid state develops at low temperatures. Thismetallic state is extremely susceptible to disorder however and localizationrapidly sets in. We show, through quantitative comparison of the relevantenergy scales, that this metal/insulator crossover occurs precisely when thescattering rate within the chain exceeds the interchain hopping rate(s), i.e.once carriers become confined to a single conducting element.

Fragile three-dimensionality in the quasi-one-dimensional cuprate PrBa_2Cu_4O_8