Charge and energy transfer by solitons in low-dimensional nanosystems with helical structure

We study the nonlinear mechanism of the energy and charge transfer in low-dimensional nanosystems with helical structure. We show that the helical symmetry is important for the formation, stability and dynamical properties of the soliton-like self-trapped electron states. We obtain several types of stationary soliton solutions, namely single-band and hybrid two-band solitons which possess different energies. The two-band hybrid soliton spontaneously breaks the local translational and helical symmetries. For the values of the parameters of α-helical proteins this soliton possesses the lowest energy as compared with other types of solitons. This soliton has an inner structure which is manifested by a modulated multi-hump amplitude distribution of excitations on the individual strands of hydrogen bonds, identified in the helix. The displacement of such a soliton along the helix reveals distinctly the complex and composite structure of the soliton and causes oscillations of the energy distributions between the strands of hydrogen bonds. We show that the frequency of these oscillations is proportional to the soliton velocity. The radiative life-time of this hybrid soliton is calculated and shown to exceed by several orders of magnitude the life-time of a soliton excitation in a three-strand macromolecule without helical structure. The other two soliton solutions are formed by single-band states. These solitons preserve the helical symmetry, but in the α-helix they are dynamically unstable: once initially formed, they transform into the ground hybrid soliton state when propagating along the chain.