Critical enhancement of thermoelectric properties with doping-induced second-order ferroelectric transition in ${\mathrm{BaTiO}}_3$

Doping a conventional ferroelectric insulator can yield intriguing changes in its electronic transport properties, in particular when a polar-to-nonpolar transition occurs. In this work, we study the effect of electron doping on the resistivity and Seebeck coefficient of the prototypical ferroelectric ${\mathrm{BaTiO}}_3$, which undergoes a tetragonal-to-cubic second-order phase transition at a critical doping concentration. The transport properties are computed using two first-principles methods: (1) The constant relaxation time approximation and (2) the fully ab initio variational approach considering explicitly electron-phonon coupling. We show that the doping effect on the transport properties is manifold, via upshift of the Fermi level, variation of the band structure (tetragonal towards cubic), and phonon softening around the transition point, which causes nonmonotonic changes of the resistivity and Seebeck coefficient, especially the anomalies close to the transition point. Results of the two methods are compared, and the effect of temperature is also discussed.