The ground state of the quasi-one-dimensional cuprate PrBa$_{2}$Cu$_{4}$O$_{8}$: field-induced dimensional crossovers and disorder-induced one-dimensionality

PrBa$_{2}$Cu$_{4}$O$_{8}$, the non-superconducting analogue of the high-$T_{c}$ cuprate YBa$_{2}$Cu$_{4}$O$_{8}$, is an extremely anisotropic quasi-one-dimensional (Q1D) metal ($t_{b}^{2}$: $t_{a}^{2}$: $t_{c}^{2} \quad \sim $ 4000: 2: 1). The in-chain ($b$-axis) charge dynamics were investigated as a function of temperature and applied magnetic field for several samples of different disorder content. Measurements in magnetic fields up to 65 T confirm the correspondence between dimensional crossovers due to magnetic field carrier confinement and temperature-induced decoherence, opening the possibility of accessing the Tomonaga-Luttinger liquid state in this material. A metal-insulator transition is observed with increasing disorder concentration for samples with nominal mean free path of $\sim $100$b$. The onset of this remarkable localisation phenomenon reveals a striking correlation between the scattering rate and the interchain hopping rate(s), suggesting a \textit{disorder}-induced crossover to a one-dimensional (1D) ground state. $b$-axis magnetoresistance measurements were performed in order to identify the nature and properties of the Q1D metallic and disorder-induced 1D insulating states.