Variational energy band theory for polarons : mapping polaron structure with the Merrifield method

Abstract

In this paper we revisit from a contemporary perspective a classic problem of polaron theory following the variational approach originally taken by Merrifield. Polaron structure is represented by a variational surface giving the optimal values of the complete set of phonon amplitudes for every value of the joint exciton–phonon crystal momentum κ. Quantities such as complete ground state energy bands (all κ) and effective masses (κ=0) are obtained. The parameter space of the problem is mapped, with careful attention given to the self-trapping transition. Through this examination of the complete parameter space at all κ, it is found that the common notion of a sharp self-trapping phenomenon associated with κ=0 is a limiting aspect of a more general finite-κ phenomenon. The idea of polaron Wannier states is addressed briefly, and the properties of such states tied to characteristics of the polaron energy band. The successes and failures of the Merrifield method are assessed.