Localized excitations in competing bond-order-wave, charge-density-wave, and spin-density-wave systems

Abstract

The characteristics of localized excitations in quasi-one-dimensional systems are rather sensitive to the interplay between the electron-phonon (e-ph) and electron-electron (e-e) interactions giving rise to competition and possible coexistence of various symmetry-broken ground states such as the bond-order wave (BOW), the charge-density wave (CDW), and the spin-density wave (SDW). Such effects are observable in halogen-bridged mixed-valence transition-metal complexes, and can be elucidated within the Bogoliubov--de Gennes formalism using an extended Peierls-Hubbard model. The coexistence of local BOW, CDW, and SDW distortions is demonstrated in this paper for polarons and self-trapped excitons (STE) in different symmetry-broken ground states. An extensive study of localized excitations over a wide range of the on-site e-ph coupling ${\ensuremath{\lambda}}_{2}$ and the Hubbard interaction U leads to the following observations. (a) As ${\ensuremath{\lambda}}_{2}$ increases at fixed U, the number of bound states inside the gap changes from two to four for the STE case and from two to three for the polaron case. (b) Upon its further increase, one type of STE with a certain pattern of SDW distortion and charge transfer is transforming into another type of STE with a different pattern. (c) A nonmonotonic dependence of the lattice relaxation energy on ${\ensuremath{\lambda}}_{2}$ is predicted within the lattice relaxation approach developed by Su and Yu earlier, and is attributed to a crossover from the weak-coupling to strong-coupling behavior showing up as the emergence of new bound states inside the gap. Moreover, the nonradiative transition rate of STE is also calculated and is used to tentatively interpret the very short lifetime of STE in PtCl complexes. Such nonmonotonic dependence of the relaxation rate on the coupling constant may also be observed in other quasi-one-dimensional systems as well.