The optical phonon resonance scattering with spin-conserving and spin-flip processes between Landau levels in graphene

In the frame of Huang–Rhys's lattice relaxation model, we theoretically investigate the electron relaxation assisted by optical phonon resonance scattering among Landau levels with spin-conserving and spin-flip processes in graphene. We not only consider the longitudinal optical (LO) phonon scattering, but also the surface optical (SO) phonon scattering induced by the polar substrate under the graphene. The relaxation rate displays a Gaussian distribution by considering the effect of lattice relaxation that arises from the electron-deformation potential acoustic phonon interaction. We find that the relaxation rate of the spin-conserving process is three orders of magnitude larger than that of the spin-flip process for the same phonon mode. Moreover, the discrepancy of relaxation rates between the SO and LO phonon scattering is at two orders of magnitude for the same process. The opposite temperature dependence of the relaxation rates are also obtained in the resonance energy regime in the present model. In addition, the influences of the strength of Rashba spin–orbital coupling, the dielectric constant of different polar substrates and the distance between the graphene and substrate on the relaxation rates are also discussed quantitatively for the SO phonon scattering. The obtained results could be useful for the graphene-based applications on the mid-infrared and terahertz modulation and spintronic devices. (paper)