We explore a novel coupling mechanism of electrons with the transverse optical (TO) phonon branch in a regime when the TO mode becomes highly anharmonic and drives the ferroelectric phase transition. We show that this anharmonicity, which leads to a collective motion of ions, is able to couple electronic and lattice displacement fields. An effective correlated electron-ion dynamics method is required to capture the effect of the onset of the local electric polarization due to this collective behavior close to the quantum critical point. We identify an intermediate temperature range where an emergent phonon drag may contribute substantially to thermoelectric conductivity in this regime. We find that, under optimal conditions, this extra contribution may be larger than values achieved so far in the benchmark material, PbTe. In the last part we make a case for the importance of our results in the generic problem of anharmonic electron-lattice dynamics.
PACS numbers:Motivated by the search for new efficient renewable sources of energy, a huge experimental effort has been made towards identifying materials with better thermoelectric properties in the recent years. So far, this intense search has been based mostly on a single particle theoretical description of electrons and standard electron-phonon coupling due to displacement potential, supported by numerical ab-initio simulations[1] [2]. While this research program has had some notable successes [3] it should be also noted that the progress has been slow and so novel pathways are needed. At the same time it has been observed that in several cases good thermoelectrics (TE) are weakly doped semiconductors, such as PbTe[4], SnTe or SrTiO 3 , that are in the vicinity of a ferroelectric quantum critical phase transition (FE-QCP). It is then natural to ask if it is just a pure coincidence, or whether an yet undiscovered mechanism enhances the Seebeck coefficient.As the system approaches the FE-QCP, a crucial role is played by the transverse optical (TO) phonons. In the Landau macroscopic framework the TO mode spectral weight is coupled to the material's electric polarization [5] (the order parameter), so as the FE transition takes place, the TO softening at q = 0 indicates the emergence of a uniform displacement and the polar order. The electrons should be susceptible to this dipole ordering and usually the appearance of the FE is accompanied by a disappearance of the electron pockets. Otherwise the remaining free electrons would screen the FE order. A massive softening at the Γ point implies that the TO branch emerges as a new family of phonons with a very substantial velocity, often comparable to the one of the longitudinal acoustic (LA) branch [6], and so they certainly contribute to the transport properties of the system.The assertion about coupling between electrons and the TO phonons is experimentally confirmed in an incipient FE, PbTe, by observation[7] that i) photoexcited electrons do change the TO phonons frequency and ii) in return these TO phonons do modify th...