Comment on "Influence of image forces on the electron transport in ferroelectric tunnel junctions"

Udalov and Beloborodov in the recent papers [Phys. Rev. B 95, 134106 (2017); Phys. Rev. B 96, 125425 (2017)] report the strong influence of image forces on the conductance of ferroelectric tunnel junctions. In particular, the authors state that there is enhancement of the electroresistance effect due to polarization hysteresis in symmetric tunnel junctions at nonzero bias. This conjecture seems to be a breakthrough --- the common knowledge is that the considerable effect, linear over voltage bias, takes place only in NONsymmetric junctions. We show that the influence of image forces on the conductance of ferroelectric tunnel junctions is highly overestimated due to neglecting the difference between characteristic ferroelectric relaxation and electron tunneling times. We argue that notable enhancement of the electroresistance effect from image forces due to polarization hysteresis in symmetric tunnel junctions at nonzero bias might be observed only at anomalously slow electron tunneling through the barrier. The same applies to magnetic tunnel junctions with a ferroelectric barrier also considered by Udalov et al: there is no significant increase of the magnetoelectric effect due to image forces for typical electron tunneling times. Udalov and Beloborodov completely missed the development of image force theory since 1950's and they forgot that electrons move much faster than atoms in condensed matter. We underline that taking into account dynamical effects in charge tunneling can bring new insight on physics of ferroelectric tunnel junctions.