The polaronic soliton in a narrow gap system

We construct a model to study the one-dimensional localized excitation, which is called a “soliton”, in a narrow-gap system. The system consists of one electron, which is described by a tight-binding Hamiltonian, and a classical diatomic molecular harmonic lattice. Both the intramolecular and intermolecular interactions between the electron and atomic lattice are included in our model. From this model, the soliton solution can be obtained analytically in the continuum limit. We find that its properties strongly depend on the gap regions where the soliton energy falls; for example, the soliton has a bell-like form when the eigenenergy is near the conduction band-edge, but a two-peak form when the eigenenergy is near the gap center. Our model is compared with the molecular-crystal model and the coupled electron–phonon model. We find that our model can be thought of as a bridge between them: the molecular-crystal model can be seen as a special case of our model, while our model can be seen as a special case of the coupled electron–phonon model in some limit. Finally, we compare the soliton in our model with the gap soliton in nonlinear optical systems and the intrinsic localized mode in the anharmonic lattice to show the similarity and difference between them. All these results are confirmed by the numerical simulations based on the transfer-matrix method.