Spin-Dependent Transport of Carbon Nanotubes with Chromium Atoms

Abstract

This paper presents a new method of describing electronic correlations in disordered magnetic crystals based on the Hamiltonian of multi-electron system and diagram method for Green’s functions finding. Electronic states of a system were approximately described by self-consistent multi-band tight-binding model. The Hamiltonian of a system is defined on the basis of Kohn–Sham orbitals. Potentials of neutral atoms are defined by the meta-generalized gradient approximation (MGGA). Electrons scattering on the oscillations of the crystal lattice are taken into account. The proposed method includes long-range Coulomb interaction of electrons at different sites of the lattice. Precise expressions for Green’s functions, thermodynamic potential and conductivity tensor are derived using diagram method. Cluster expansion is obtained for density of states, free energy, and electrical conductivity of disordered systems. We show that contribution of the electron scattering processes to cluster expansion is decreasing along with increasing number of sites in the cluster, which depends on small parameter. The computation accuracy is determined by renormalization precision of the vertex parts of the mass operators of electron-electron and electron-phonon interactions. This accuracy also can be determined by small parameter of cluster expansion for Green’s functions of electrons and phonons. It was found the nature of spin-dependent electron transport in carbon nanotubes with chromium atoms, which are adsorbed on the surface. We show that the phenomenon of spin-dependent electron transport in a carbon nanotube was the result of strong electron correlations, caused by the presence of chromium atoms. The value of the spin polarization of electron transport is determined by the difference of the partial densities of electron states with opposite spin projection at the Fermi level. It is also determined by the difference between the relaxation times arising from different occupation numbers of single-electron states of carbon and chromium atoms. The value of the electric current spin polarization increases along with Cr atoms concentration and magnitude of the external magnetic field increase.