RKKY interaction in spin polarized doped zigzag carbon nanotube in Holstein model

Abstract

We have theoretically studied the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in zigzag gapped graphene nanotube in the presence of Holstein phonons . We investigate the effect of quantities such as the gap parameter, intensity of the electron-phonon interaction, nanotube diameter, next nearest neighbor hopping parameter, chemical potential, etc. on the spatial behavior of the RKKY interaction. Since the RKKY interaction can be obtained from the static spin susceptibility function, we first need to calculate this function. The spin susceptibility is calculated using Green's function approach via computing the correlation function of spin density operators for the Holstein model Hamiltonian. We also exploit the random phase approximation (RPA) to correct the spin susceptibility function using the self energy due to the electron-phonon interaction. The results indicate an oscillating behavior for the spatial dependence of the RKKY interaction. It is also clear that the mentioned quantities listed above affect the spatial behavior of RKKY interaction. • Using Holstein model Hamiltonian, the excitation spectrum of electrons on nanotube has been found. • To obtain RKKY interaction, the spin susceptibility has been calculated using Green's function approach in Holstein model. • We have the effects of diameter, electron-phonon coupling and electron doping on the RKKY interaction in zigzag nanotube. • Results show an oscillating behavior for spatial dependence of coupling exchange constant between two local impurities.