Electron Polarization Solitons in a Helical Molecule

Abstract

The evolution of the spin of an electron moving along the axis of a long helical molecule under the action of an external field is investigated. The field is produced by the dipoles of individual molecules forming a complex molecular structure (e.g., a DNA molecule). The electron polarization dynamics associated with the spin–orbit interaction is described using an integrable generalization of the Manakov equations. The phase cross-modulation, self-modulation, and analogs of the Rashba and Dresselhaus Hamiltonians are taken into account in the model Hamiltonian. The corresponding apparatus based on the solution of the Riemann–Hilbert problem is used for obtaining soliton solutions. The resultant one- and two-soliton solutions demonstrate a number of new properties. It is shown that a local perturbation produces a selective effect on the soliton polarization and can be used for controlling the position of the electron spin using impurity molecules or quantum dots with a constant dipole moment. It is found that the spin–orbit interaction leads to a strong spatial modulation of the soliton shape. The collision of solitons leads to modulation transfer between solitons and a change in the modulation amplitude.