  We propose a theoretical model of a ferroelectric metal where spontaneous
electric polarization coexists with the conducting electrons. In our model we
adopt a scenario when conducting electrons interact with two soft transverse
optical phonons, generalize it to the case when there is a spontaneous
ferroelectric polarization in the system, and show that a linear coupling to
the phonons emerges as a result. We find that this coupling results in
anisotropic electric transport which has a transverse to the current voltage
drop. Importantly, the obtained transverse component of the resistivity has
distinct linear dependence with temperature. Moreover, we show that the
coupling enhances superconducting transition temperature of the ferroelectric
metal. We argue that our results help to explain recent experiments on
ferroelectric strontium titanate, as well as provide new experimental
signatures to look for.
