Abstract
A modified one-dimensional nonlinear Schr\"odinger equation which includes off-diagonal nonlinearity is proposed to describe the behavior of electrons via electron-phonon couplings in the Su-Schrieffer-Heeger Hamiltonian. We find an interesting self-trapping phenomenon of electrons which takes place when the magnitude of the nonlinearity parameter is close to the value of the hopping integral. For a periodic lattice, the ballistic propagation of a wave packet is found in this modified one-dimensional nonlinear Schr\"odinger equation, and the propagation rate increases with the increase of nonlinearity parameter except in the self-trapping interval. When diagonal disorder is introduced, the electronic states are localized, and no delocalization effect of the off-diagonal nonlinearity is found. These results are quite different from that in the diagonal nonlinear lattice, where delocalization is found.
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