On soliton-Mediated Fast Electric conduction in a Nonlinear Lattice with Morse Interactions

In a previous letter [Velarde et al., 2005] a new form of electric conduction mediated by solitons was shown to be possible in an anharmonic Toda lattice. In the presence of an external electric field this current can be much higher than the Drude-Ohm linear current and, as the field is lowered, the current achieves a finite, constant, field-independent value. The model studied therein is strictly classical. The electron-ion (lattice) interaction is Coulombic, albeit with an appropriate pseudopotential. The lattice interactions are of Toda type [Toda, 1989], hence allowing for phonon — and soliton — longitudinal vibrations with compressions governed by the repulsive part of the potential [Chetverikov et al., 2005a, 2005b]. These compressions were shown to be responsible for electron trapping (or electrostatic “localization”) by the lattice ions, and the formation of dynamic bound states (solectrons) of the electron with the soliton (the cnoidal wave moving through the lattice). The phenomenon discovered is similar to surfing on a bore as it travels along a river. The surfer ought at an appropriate time to be ready to go on top of the bore and, on the other hand, the bore (call it “topological” soliton) travels rapidly upstream, at a constant speed relative to the downstream flow. In the present letter we pursue the same idea in view of applying the results to a more realistic situation. We improve upon the previous model by replacing the classical electrostatic trapping with the quantum mechanical “tight binding” approximation, currently in use in solid state physics [Ashcroft & Mermin, 1976; Heeger et al., 1988; Yu, 1988]. Furthermore, we replace the Toda interaction, which has unphysical aspects (particularly its attraction), with the Morse interaction, akin to the Lennard–Jones interaction [Choquard, 1967; Chetverikov et al., 2005c]. Figure 1 compares these two interaction potentials, as well as the Toda potential. Figure 2 shows how the Morse interaction approaches the Toda interaction felt by an ion from its nearest neighbors, when repulsion dominates the dynamics, a feature we shall make use of later on (the harmonic case is also depicted for