An analytic study of the E ⊗ e Jahn-Teller polaron

An analytic study is presented of the E⊗e Jahn-Teller (JT) polaron, consisting of a mobile eg electron linearly coupled to the local eg normal vibrations of a periodic array of octahedral complexes. Due to the linear coupling, the parity operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} and the angular momentum operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} commute with the JT part and cause a twofold degeneracy of each JT eigenvalue. This degeneracy is lifted by the anisotropic hopping term. The Hamiltonian is then mapped onto a new Hilbert space, which is isomorphic to an eigenspace of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} belonging to a fixed angular momentum eigenvalue j > 0. In this representation, the Hamiltonian depends explicitly on j and decomposes into a Holstein term and a residual JT interaction. While the ground state of the JT polaron is shown to belong to the sector j = 1/2, the Holstein polaron is obtained for the “unphysical” value j = 0. The new Hamiltonian is then subjected to a variational treatment, yielding the dispersion relations and effective masses for both kinds of polarons. The calculated polaron masses are in remarkably good agreement with recent quantum Monte Carlo data. The possible relevance of our results to the magnetoresistive manganite perovskites is briefly discussed.