Dionys Baeriswyl

An Overview of the Theory of π-Conjugated Polymers

We review recent advances in the theoretical modelling of π-conjugated polymers. Our emphasis is on quasi-one-dimensional π-electron models that include both electron-phonon and electron-electron interactions. We use the widely studied Peierls-Hubbard Hamiltonian as a prototype model, since this contains both the pure electron-phonon (Huckel and SSH) limits and the pure electron-electron (Hubbard and PPP) limits. We attempt to present an integrated perspective by explaining the essential concepts in both chemical language (valence bonds, resonance, bond alternation defects, etc.) and solid-state physics terms (band structure, localized states, broken symmetry, solitons). We argue that modelling π-conjugated polymers is a true many-electron problem requiring advanced techniques that give reliable answers to precise questions, especially for excited states. Among the techniques we discuss are mean-field, perturbative, and variational approximations for infinite polymer chains and (numerically) exact computations (Lanczos and quantum Monte Carlo methods) for finite chains (oligomers). We compare critically the theoretical results obtained by these various methods with experimental observations, in particular with optical spectroscopy and nuclear magnetic resonance, both for the archetypal π-conjugated system polyacetylene and for other conjugated polymers including polydiacetylenes and polythiophene. Our goal is to find a model consistent with the broad range of experimental data. This analysis establishes that electron-phonon and electron-electron interactions are likely to be of equal importance in determining the properties of these materials. Hence neither the Huckel/SSH nor the PPP/Hubbard models are sufficient for a complete description of the observed behaviour of π-conjugated polymers. We add an analysis of factors that go beyond the idealized models, including disorder, inter-chain coupling and quantum lattice fluctuations, and conclude with a brief discussion of the dopinginduced insulator-metal transition and of the possible mechanisms of charge transport.

Electron-electron interaction effects in quasi-one-dimensional conducting polymers and related systems

Abstract We review recent results on the role of electron-electron (e-e) interactions in quasi-one-dimensional conducting polymers and related systems. Within the Peierls-Hubbard model, the effects of both short-range (on-site U and nearest neighbor V 1 ) and long-range ( V j , j ≥ 2) are examined, the former using quantum Monte Carlo and the latter with exact diagonalization of finite size systems and analytic arguments. We also discuss optical absorption properties in the presence of electronic correlation, focusing on the weak and strong coupling limits.

Statics and adiabatic dynamics of non-linear excitations in defected polyacetylene

Abstract Within the Su, Schrieffer and Heeger model we have calculated, both analytically and numerically, the effects of model impurities on the electronic structure and lattice distortion of trans -polyacetylene. We find that the electron-phonon coupling may result in a fundamental alteration of the impurity level location for sufficiently strong impurities. In simulated photoexcitation experiments on the defected system, we find that, in addition to the kinks and breathers produced in the undefected system, ‘trapped kinks’, excitons and polarons may also be produced (for impurities of sufficient strength). We suggest that the polarons produced in this novel way may be unusually stable and play a role in hopping conduction mechanisms.

Coulomb correlation effects in quasi-one-dimensional conductors

Abstract We review recent results on the role of electron-electron (e-e) interactions - “correlation effects” - in quasi-one-dimensional conductors. Within the Peierls-Hubbard model, we examine the consequences of short range (on-site U and nearest neighbor V) e-e interactions for ground state properties, nonlinear excitations, and optical absorption. Our techniques include quantum Monte Carlo and weak and strong coupling perturbative arguments.

Impurities and nonlinear dynamics in models of conjugated polymers

Abstract We describe adiabatic statics and dynamics for electron-phonon coupled models of several linear conjugated polymers, including trans - and cis -polyacetylene, ordered A–B alloys, and site- and bond-defected systems. The ubiquitous role of “breathers” is emphasized, as well as striking renormalizations of intragap localized electronic levels.

The role of electron-electron interactions in conducting polymers

Abstract A few general concepts of the many-electron problem and some specific effects of Coulomb interactions in conjugated polymers are summarized. The emphasis is on key experiments, mostly on the best studied material polyacetylene.

Nonlinear Adiabatic Dynamics In Polyacetylene and Related Materials

Abstract Numerical and analytical studies of the dynamic, mean-field, adiabatic Su-Schrieffer-Heeger model of polyacetylene are shown to reveal the typical importance of strong, coherent anharmonicity, e.g. as “breathers”. Examples illustrated include (i) single kink dynamics, (ii) electron-hole (e-h) decay in trans-(CH)x; (iii) e-h decay in cis-(CH)x; (iv) e-h decay in linear polyynes; (v) decay of a photoexcited kink or polaron; (vi) photoexcitation in the presence of bond or site defects. Using a variety of examples we have shown that the adiabatic dynamics of the SSH electron-phonon model typically exhibits strongly coherent anharmonic excitations, e.g. “breathing” modes. We have emphasized situations, e.g. photoexcitation, in which the energy input is high. Breather generation with spallation neutrons should also be considered, as should thermal production in materials with narrower band gaps. Persistent, localized breathers will also be typical in the presence of “confinement” mechanisms –whether du...