Influences of RSO interaction and LO phonon effect on the spin polarization state energy of polaron in a quantum rod

Abstract

On the basis of Lee-Low-Pines unitary transformation, the influences of Rashba spin–orbit (RSO) coupling energy and Zeeman splitting energy on the ground-state energy of polaron in a quantum rod (QRD) have been studied by using a variational method of Pekar type. Taking the RSO interaction and the Zeeman splitting into account, we derive the variational relations of the absolute ratios \( \zeta_{1} \) and \( \zeta_{2} \) of the RSO coupling energy and the Zeeman splitting energy to the ground-state energy of polaron with the transverse confinement radius (TCR) and the longitudinal confinement length (LCL) of QRD, as well as and the magnetic field adjusting length (MFAL). The results show that the absolute ratios \( \zeta_{1} \) and \( \zeta_{2} \) will increase when the TCR and the LCL become larger, but will slowly decrease while the MFAL and the aspect ratio of the ellipsoid \( \delta \) increase, respectively. The above results can be attributed to the spin effects and interesting quantum size confining.