Variational energy band theory for polarons : mapping polaron structure with the Toyozawa method
Brown, David W.
Date of Issue1997
School of Materials Science and Engineering
In this article we revisit from a contemporary perspective a classic problem of polaron theory in one space dimension following the variational approach originally taken by Toyozawa. Polaron structure is represented by variational surfaces giving the optimal values of the complete set of exciton and phonon amplitudes for every value of the joint exciton-phonon crystal momentum κ. Through this exfoliation of the exciton-phonon correlations comprising the polaron, characteristic small polaron, large polaron, and nearly free phonon structures are identified, and the manner in which these compete and/or coexist is examined in detail. Through such examination, the parameter space of the problem is mapped, with particular attention given to problematic areas such as the highly quantum mechanical weak-coupling regime, the highly nonlinear intermediate-coupling regime, and to the self-trapping transition that may be said to mark the onset of the strong-coupling regime. Through such examination of the complete parameter space at all κ, it is found that the common notion of a self-trapping phenomenon associated with κ=0 is a limiting aspect of a more general finite-κ phenomenon. Quantities such as phonon number distributions, complete ground state energy bands, and effective masses are obtained for all κ. The inverse problem of associating localized functions with the variational energy bands is addressed, with attention given to the concept of solitons and with the explicit construction of polaron Wannier states. The successes and failures of the Toyozawa method are assessed.
DRNTU::Science::Physics::Atomic physics::Solid state physics
Journal of chemical physics
© 1997 AIP. This paper was published in Journal of Chemical Physics and is made available as an electronic reprint (preprint) with permission of American Institute of Physics. The paper can be found at: [Doi: http://dx.doi.org/10.1063/1.474668]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.