Analytical properties of a (Wannier) exciton-phonon system: On the exclusion of self-trapping and overscreening

We perform a critical analysis of the concept of phonon-induced phase transitions in connection with (Wannier) exciton-phonon systems. Particular attention is paid to the frequently discussed phenomena of self-trapping and overscreening. We demonstrate for a large class of (generalized Fröhlich) models that a phase-transition-like behavior can be excluded: The ground-state energy, ground-state wave function, and the formal free energy are smooth functions of the electron-phonon and electron-hole coupling parameters. Analogous results hold for a magnetoexciton-phonon system, moving unrestricted or, e.g., within a quantum well. Our proof makes use of functional-analytic and functional-integral methods, which have been successfully applied in previous studies of polaron systems.