Electron-correlation effects in one-dimensional large-bipolaron formation.

Abstract

We study the effects of electron correlation on the ground state of a one-dimensional large singlet bipolaron. The electron-lattice interaction is taken to be the short-range interaction of Holstein's molecular-crystal model. We represent the Coulomb repulsion with the Hubbard short-range repulsion. This adoption of the Hubbard model is equivalent to replacing a strict one-dimensional system that has a short-range logarithmic divergence of the Coulomb repulsion energy between overlapping charges, with a quasi-one-dimensional system of finite width. Two types of electronic correlation are considered. With ``in-out'' correlation, we permit one of the two self-trapped carriers of the bipolaron to have a larger radius than the other. With ``left-right'' correlation, we permit the centroids of the self-trapped carriers to be displaced from one another. For both types of correlation, variational calculations are performed to determine the magnitudes of the correlation effects in the ground state. There are three parameters in the model: the electronic bandwidth parameter t, the electron-lattice coupling strength ${\mathit{E}}_{\mathit{b}}$, and the Hubbard repulsion, ${\mathit{V}}_{\mathit{c}}$. The electron-lattice interaction provides an indirect intercarrier attraction that fosters the coalescence of the two carriers. In opposition, the carriers' Coulomb repulsion and the kinetic energy required for carrier confinement foster the carriers spreading. With bipolaron formation the intercarrier attraction dominates the Coulomb repulsion.The electron-correlation effect on the bipolaron's binding depends explicitly on only ${\mathit{V}}_{\mathit{c}}$/${\mathit{E}}_{\mathit{b}}$. The electron correlation also depends on the shape of the local functions presumed in the variational calculations. Of course, the effects of electron correlation on the bipolaron's ground state increase as the Coulomb repulsion between the carriers is increased. Strikingly, we also find that the dependence of the confinement energy on electronic correlation is critical to promoting electronic correlation in the bipolaron's ground state. This feature is discussed in detail. At a maximum ratio of ${\mathit{V}}_{\mathit{c}}$/${\mathit{E}}_{\mathit{b}}$ for which we have stable bipolarons, we find that electronic correlation can lower the ground-state energy of our bipolaron by up to 30%.