Variable-range hopping and positive magnetoresistance in insulating ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Pr}}_{\mathit{x}}$${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ crystals

We have measured in-plane resistivity and magnetoresistance of insulating ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Pr}}_{\mathit{x}}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ (x∼0.63) crystals in magnetic fields up to 8 T. Mott variable-range-hopping transport ρ=${\mathrm{\rho }}_0$ exp{(${\mathit{T}}_0$/T${)}^{\mathrm{\alpha }}$} has been observed with α=1/4 at low temperatures suggesting the metal-insulator transition caused by Pr doping is due to carrier localization. The magnetoresistance in the Mott variable-range-hopping regime is found to be positive and anisotropic, which may be caused by a decrease of the localiztion length induced by the magnetic field.