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Analytical properties of polaron systems or: Do polaronic phase transitions exist or not?

B. Gerlach and H. Löwen

B. Gerlach

  • Institut für Physik der Universität Dortmund, 4600 Dortmund 50, Germany

H. Löwen

  • Sektion Physik der Universität München, 8000 München 2, Germany

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Rev. Mod. Phys. 63, 63 – Published 1 January, 1991

DOI: https://doi.org/10.1103/RevModPhys.63.63

Abstract

For more than 40 years it was thought that polaron- and exciton-phonon systems exhibited unexpected localization properties. Particular attention was paid to the so-called phonon-induced self-trapping transition, which, it was believed, should manifest itself as a point of nonanalyticity in the ground-state energy as a function of the electron-phonon coupling parameter. It will be demonstrated for a large class of (generalized Fröhlich) models that no such transition exists. The dimensionality of space has no qualitative influence; insofar, an application of the authors' results to problems in lower dimensions (e.g., polarons in quantum wells) is straightforward. The same holds true if homogeneous external fields are involved; for example, a discontinuous mass stripping for magnetopolarons can be excluded. On the other hand, a phase-transition-like behavior will be found, if a polaron or exciton is exposed to a short-range potential, allowing a so-called pinning transition. The authors emphasize, however, that even in this case the transition is only modified, and not induced, by phonons.

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Rev. Mod. Phys. 63, 63– Published 1 January, 1991

    © 1991 American Physical Society

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