Bipolaron

Abstract

Polarons interact with each other, cf. (3.40) for small polarons. The range of the deformation surrounding the Fröhlich polarons is quite large, and their deformation fields are overlapped at finite density. Taking into account both the long-range attraction of polarons owing to the lattice deformations and their direct Coulomb repulsion, the residual long-range interaction turns out rather weak and repulsive in ionic crystals [26]. In the long-wavelength limit $(q \ll \pi/a),$ the Fröhlich EPI dominates in the attractive part, but polarons repel each other at large distances, $|{\rm m}- {\rm n}| \gg a$:

$$v({\rm m} - {\rm n}) = \frac{e^{2}}{\varepsilon_0|{\rm m} - {\rm n}|} > 0.$$

(4.1)

The Fröhlich EPI nearly nullifies the bare Coulomb repulsion, if $\varepsilon_0 \gg 1,$ but cannot overscreen it at large distances.