Spin polaron in a chiral molecule with an all quantum model

Recently, the chiral induced spin selectivity (CISS) has been demonstrated in different systems such as DNA, proteins, bacteriorhodopsin, helicene and other chiral molecules. In this phenomenon, the spin of the carriers will couple with the chirality of the system and exhibit special transport properties. The explanation of the mechanisms of CISS is still under debating, but it generally accepted that the chirality-induced spin-orbit coupling and the environment play pivotal roles. In addition, in such systems with strong electron-phonon coupling, the moving electrons and holes would interact with phonons to construct polarons as carriers. Therefore, to understand CISS it is needed to focus on the spin-related transport of the polarons. In this paper, we investigate the spin-charge property of a carrier in a chiral helix molecule described with an all-quantum model. Both the extended electron and bound states are obtained analytically. Our findings indicate that the spin and momentum of these carriers are locked, with the nature of this coupling being dictated by the chirality of the system. This work provides valuable insights for theoretical investigations into nonlinear equations and contributes to a deeper understanding of chiral carriers in the context of the CISS effect. Our solution is instructive for theoretical investigation on nonlinear excitations and our results shed new light on the chiral carriers to understand CISS effect.