Two-site polaron problem: Electronic and vibrational properties

Abstract

A complete numerical solution is given for the two-site polaron problem: electrons hopping between two adjacent diatomic molecules to which they couple via a charge-density--intramolecular-deformation interaction of strength \ensuremath{\alpha}. As one enters the polaronic regime upon increasing \ensuremath{\alpha}, the quasiparticle picture for the electrons breaks down. This is manifest in the appearance of a broad spectrum in the spectral functions due to (i) strong nonlinear mixing of electronic and vibrational degrees of freedom and (ii) the intrinsic attractive interaction between small polarons leading to their instability towards pair formation. These effects, which are signatures of polarons, can be measured by photoemission spectroscopy for the electrons and are visible in the inelastic-neutron-scattering cross section for the phonons. A number of other measurable effects are discussed as a function of temperature: the anomalous temperature behavior of the vibrational energy of the molecules (resonant neutron absorption spectroscopy), the radial distribution function for the intramolecular distance showing fluctuations between two preferential distances (x-ray-absorption fine structure), and the mean-square displacements of the atoms in the molecules (Debye-Waller factor). Links with experiments on polaronic systems are made.