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In the context of the massless Nelson model, we prove that two non-relativistic nucleons interacting with a massless meson field do not bind when a sufficiently strong Coulomb repulsion between the nucleons is added to the Hamiltonian. The result holds for both the renormalized and unrenormalized theories, and can also be applied to the so-called piezoelectric polaron model, which describes an electron interacting with the acoustical vibrational modes of a crystal through the piezoelectric interaction. The result can then be interpreted as well as a no-binding statement about piezoelectric bipolarons. The methods used allow also for a significant reduction of about 30% over previously known no-binding conditions for the optical bipolaron model of H. Fröhlich.

The normal states of simple elemental metal and complex compound superconductors have been studied by using first principle methods and model analysis. The flat/steep band electronic structure and the peak-like structure of electron-phonon coupling have been found as two universal characteristics. A new Hamiltonian is proposed to describe the electronic structure of insulating solids.

Bipolaron dynamics in non-degenerate polymers are discussed using the nonadiabatic dynamic method. First, charge injection process from metal electrode to a nondegenerate polymer in a metal/polymer/metal structure has been investigated. We demonstrate that the dynamical formation of a bipolaron sensitively depends on the work function of metal electrode. We also study the bipolaron dissociation process. It is found that the electric field that can dissociate the bipolaron is up to 10⁶ V/cm, which is consistent with experiments.

Both polarons and bipolarons are composite particles with internal structures in nondegenerate conjugated polymers. A bipolaron is a spinless species with charge ±2|e|, while a polaron is a spin-bearing one (spin 1/2, charge ±|e|). Serving as charge carriers, they play an important role in the transport properties of polymer-based optoelectronic devices. By using a nonadiabatic dynamic method, the motion of a bipolaron under an external electric field is theoretically investigated in a conjugated polymer with magnetic impurities. Our results show that a bipolaron can pass through the magnetic impurities, or break down into two polarons with different spins, or be trapped by the magnetic impurities, depending on the width of the impurity region. When the width of the impurity region is comparable to the polaron width, the bipolaron is transformed into two polarons easily. As a polaron and a bipolaron possess different spin characteristics, the decomposition of bipolarons induced by the magnetic impurities may have important effect on the spin polarized transportation.