Abstract
It is shown that an electron and a hole interacting mutually through the Coulomb force in the acoustic-phonon field take, within the adiabatic approximation, four possible phases depending upon the coupling constants: the lowest state is the free exciton in phase[I], the large-radius self-trapped exciton in [II], the small-radius self-trapped exciton in [III+], and a pair of self-trapped electron and self-trapped hole in [III−]. The center-of-mass motion of exciton changes discontinuously to be self-trapped as one moves from [I] to [II] or [III+] with increase in the phonon-coupling constants. The relative motion of exciton changes discontinuously to be self-shrinked as one moves from [I] or [II] to [III+]. [III+] and [III−] are realized respectively for the same and opposite sign of the deformation potentials of electron and hole. When the Coulomb interaction energy is so large as to be comparable to the electron and hole band widths, discontinuous boundary between [II] and [III+] disappears.
