Effect of electronic correlation on the shape of a large bipolaron: Four-lobed planar large bipolaron in an ionic medium

The shape of a large bipolaron is considered for self-trapped carriers confined within a plane that is immersed within a strongly ionic medium. For a wide enough electronic energy band, correlation effects determine a large bipolaron's shape. Then a stable large bipolaron is found in which the two self-trapped carriers occupy mutually perpendicular dumbbell-shaped orbitals. This arrangement gives the self-trapped carriers a planar four-lobed charge density. With progressively narrower electronic bands, the short-range electron-lattice interactions become increasingly important. Then the stable solution shifts to that of a large bipolaron with a circularly symmetric shape. With a still narrower electronic band, the stable solution collapses to that of a small (single-site) bipolaron. Thus, there can be at least three types of stable planar bipolarons in an ionic medium: (1) a four-lobed large bipolaron, (2) a circularly symmetric large bipolaron, and (3) a small bipolaron. The forces between noncircularly symmetric bipolarons depend on their shapes and relative orientations. As a result, large bipolarons' shapes can affect how and if they order in their ground state