Study of the one-dimensional periodic polaron structures

One-dimensional and quasi one-dimensional electron structures are of applied interest. For example, in one-dimensional (nano-capillary) electroneutral metal–ammonia systems, exotic electron properties are observed, such as a drastic (by several orders of magnitude) drop of the electrical conductivity with decreasing temperature, which resembles the superconductivity transition. In this work, we studied the possibility of one-dimensional filamentary polaron nano-structure in insulating media. It was established that the interpolaron pair potential for large polarons offers attraction properties. It is known that attraction between the particles may alter the collective properties of a many-particle system. We demonstrated that the initially uniform distribution of the particles becomes unstable in one-dimensional systems and may change to the nonuniform structured state under specific conditions imposed on the temperature, particle concentration, and parameters of the pair interpolaron potential. The possibility of existence of a periodic one-dimensional structure of small-amplitude polarons that is imposed on the polaron uniform distribution is estimated in terms of temperature and concentration criteria. A dispersion relation between existence of the one-dimensional polaron structure and translational velocity of the polarons is found. The upper limit of the translational velocity when the periodic contribution to the distribution vanishes is determined. Periodic contribution disappears virtually stepwise as the velocity approaches its critical value. It is shown that this specific polaron–polaron interaction leads to results that are in principal different from those observed for classical Coulomb electron interaction.