Size effect on variable-range-hopping transport in PrBa2Cu3O7−x

Abstract

Normal transport properties and their size effect of ${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ are studied using planar-type junction specimens. The transport properties of ${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ are in accordance with a variable-range-hopping mechanism. The localized wave function for this conduction has a decay length of 8.5 nm, and the hopping distance is 96 nm at 2 K. The conductance properties of junctions with a length of a few times the hopping distance show a size effect. A Coulomb correlation gap is observed at temperatures lower than 4 K, and the minimum conductance at the Coulomb gap depends weakly on temperature and magnetic field.