Analytic Study of the E ⊗ e Jahn–Teller Polaron

Abstract

A review is given of recent work on the E ⊗ e Jahn–Teller (JT) polaron, i.e., a mobile e_g electron linearly coupled to the local e_g normal vibrations of a periodic array of octahedral complexes. The main ingredient of our theory is a mapping of the Hamiltonian onto a new Hilbert space, 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. The ground state of the JT polaron belongs to the sector j = 1/2, whereas 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, effective masses and band widths for both kinds of polarons. The calculated polaron masses are in remarkably good agreement with recent quantum Monte Carlo data.