NEW ELECTRONIC LOCALIZED STATES AT A SOLITON IN SSH MODEL

As the TLM model is continuum limit of the SSH model, it is sometimes important to know corrections to the limit. We get the correction terms in a form of power series with respect to a/xi, alpha and xi being the lattice constant and the soliton width, respectively. The first order corrections have been obtained by the perturbation method. The straightforward second order perturbation calculation involves a divergence which is closely associated with an electronic localized level which has been found by numerical works below the bottom of the valence band. Since this level is induced by the first-order Hamiltonian, we propose a method which uses the sum of the zeroth- and first- order Hamiltonians as an unperturbed Hamiltonian to obtain the localized level analytically. The energy and the wave function of the localized level agree fairly well with the numerical results. The wave functions of extended electronic states are also obtained. Phase shift analysis gives consistent results with the existence of the localized state which has even parity. It further shows that the effective potential for the electrons, due to the presence of the soliton, is reflectionless except for the electrons near the band edges. These results also agree well with the numerical works.