Variational energy band theory for polarons : mapping polaron structure with the global-local method

Abstract

In this paper we revisit from a contemporary perspective a classic problem of polaron theory in one dimension using a new variational approach generalizing that of Toyozawa, based on delocalized trial states including mixed gobal and local exciton-phonon correlations. 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. 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. Complete energy bands are presented in illustrative cases, and the principal trends in the ground-state energy, polaron bandwidth, and effective mass are identified. The internal structure of our variational Bloch states is examined for qualities that might reflect the typical characteristics of solitons, finding some intriguing qualitative comparisons, but little that bears close scrutiny.