Energy of interaction between polarons and spatial configuration of bipolaron in two-dimensional systems

Abstract

The work is aimed at studying the influence of correlation effects on the interaction energy of two-dimensional (2D) polarons. The two-center configuration of 2D bipolaron corresponds to a shallow secondary minimum, which occurs when only the correlations associated with the permutation symmetry of the system are taken into account. The correlations associated with the direct dependence of the electron wave function on the distance between electrons lead to stabilization of the one-center configuration, and the secondary minimum corresponding to the two-center configuration disappears. Variational calculations were performed using a multiparameter Gaussian functions with correlation multipliers. The ground state energy of bipolaron is E2 = –0.542169 Eh* for η = ε∞/ε0 = 0, where ε∞ and ε0 are the high-frequency and static dielectric constants of the crystal, respectively, Eh* is the effective Hartree energy. The binding energy of bipolaron was calculated with respect to the double energy of 2D polaron obtained for wave function, consisting of 5 Gaussian exponents. The ground state energy of 2D polaron is E1 = –0.202366 Eh* for η = 0. The critical value of the ionicity parameter η corresponds to ηс ≈ 0.2. At η > ηc, 2D bipolaron breaks up into two 2D polarons.

Keywords

• 2d-polaron
• 2d-bipolaron
• low-dimensional systems
• electron-phonon interaction