Electric-field activated variable-range hopping transport in ${\mathrm{PrBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

We demonstrate the transport of charge carriers in ${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ (PBCO) to be dependent both on the applied electric field and on the temperature. In our measurements we use inert noble-metal contacts on laser ablated and sputtered PBCO films. By applying the transmission line model we are able to separate the contact resistance from the PBCO resistance. The average hopping distance can be found by extending Mott’s formula to field activation, and is found to be much greater than the dimensions of the PBCO unit cell. From the measurements in strong electric field a minimum hopping distance in the direction of the applied field of about 14 nm is determined, which we discuss in terms of localized states and intrinsic mixed valence of the Pr atoms in the PBCO film.