Electronic transport properties of PbTiO$_{3}$/SrRuO$_{3}$ superlattices*

First principles calculations on PbTiO$_{3}$/SrRuO$_{3}$ superlattices indicate that even when the SrRuO$_{3}$ layers in these structures are only a single unit cell thick they retain a metallic character. In the out of plane direction the resistivity of the structures are expected to depend on the thickness of the PbTiO$_{3}$ layers which act as ferroelectric tunneling barriers. We have successfully fabricated high quality specimens of these superlattices using off axis RF magnetron sputtering and here we report on their transport properties. In the out of plane direction, as well as showing ferroelectric polarization-field hysteresis loops, the samples reveal tunneling characteristics that confirm that the SrRuO$_{3}$ layers do indeed retain their metallicity in the experimental realization of these structures. In addition to studying the effect of changing the thickness of the PbTiO$_{3}$ layers in the superlattice we have examined the impact that the ferroelectric polarization and the compositionally broken inversion symmetry have on current-voltage characteristics.