Spin-orbit coupling in singly chargedπ-conjugated polymers

Abstract

Understanding spin-orbit coupling in singly charged $\ensuremath{\pi}$-conjugated polymer chains is of basic importance to the study of spin transport in organic semiconductors. We show that the spin-orbit coupling is quenched to first order because the diagonal matrix elements vanish and the energy levels in polymers are orbitally nondegenerate. Even the off-diagonal matrix elements are zero or negligibly small unless a twisted nonplanar polymer chain is considered. For such a twisted chain, we calculate these matrix elements using tight-binding wave functions based on ${p}_{z}$ orbitals. We show that the Kramers degeneracy prevents the spin-orbit-induced spin precession. Instead, we propose a phonon-assisted spin-flip process and calculate its rate.