Polarons and bipolarons in two-dimensional systems

Abstract

Polarons and bipolarons in two-dimensional (2 D) crystals with a simple conduction band are considered in the work. A study of the potential of pair interaction for the singlet states of polarons was carried out in the region intermediate coupling. The effective functional of exchange-coupled pair of polarons was obtained by the Buimistrov-Pekar method. Variational calculations of the singlet states energies were carried out taking into account the direct dependence of the wave function of the system on the interelectron distance. The variational functions have been selected in the form of a multiparameter system of Gaussian functions with exponentially correlated multipliers. The region of existence of a two-dimensional bipolaron was determined as a function of the crystal parameters. It has been shown that a single-center configuration (a configuration similar to a two-dimensional helium atom) is stable. The minimum corresponding to the two-center configuration (“polaron molecule”) is secondary extremum that disappears when the electronic correlations associated with the direct dependence of the wave function of the system on the distance between electrons are taken into account. The main energy minimum corresponds to single-center configuration. The study of the fulfillment of the virial theorem for polaron and bipolaron functionals was carried out. The results of variational calculations were compared with the calculations performed by other authors. Two-center configuration of a 2D bipolaron is unstable. The only minimum corresponds to a one-center 2D bipolaron. Exchange energy of two 2D polarons is antiferromagnetic.