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Method is developed for self-consistent calculation of the energy spectrum of free energy and electrical disordered crystals. Processes of electron scattering on the ionic core potential of different sort, fluctuations of charge, spin density and lattice vibrations are taken into account. Electronic states of the system are described using tight binding multiband model. The nature of the spin-dependent electron transport of carbon nanotubes with chromium atoms adsorbed on the surface is explained. The value of the spin polarization of electron transport is determined by the difference of the partial densities of states of electrons with opposite spin projection at the Fermi level and the difference between the relaxation times of electron states. The value of the spin polarization of the electric current increases with increasing of Cr atoms concentration and magnitude of the external magnetic field .

After a relatively recently discovered phenomenon of spin-dependent transport research of electrons spin polarization became actual [

In our work, on the basis of a self-consistent tightbinding model electronic structure, free energy, conductivity and spin-dependent transport of carbon nanotubes with chromium impurity are investigated. Electron scattering on potentials of the ionic cores of different types, and the fluctuations of the spin of the electron density and lattice vibrations are taken into account.

In present literature, the studies of spin-dependent transport in carbon nanotubes are qualitatively described on the basis of ideas about the appearance of a gap in energy spectrum near Fermi level [

The method of calculation of the energy spectrum of electrons and phonons, free energy and electrical conductivity of disordered crystal described in [

Electronic correlations in crystals are described in the multi-zone model of strong coupling. Considered the processes of electron scattering on the potential of ionic skeleton, fluctuations of the charge and spin density and lattice vibrations.

Using the formula Kubo, diagram technique for two-time temperature Green’s function and neglecting the contribution of scattering processes on clusters of three or more sites for static electrical conductivity tensor we can get the expression [

where

The first component in the right-hand side of expression (1) describes the contribution of electroconductivity approximation in the coherent potential. Other components describes the contribution in electroconductivity processes of electrons scattering on clusters consisting two atoms.

In the formula (1) component

where

Operator

To simplify the formula (1) we use approximate expression for averaged value

In formula (1):

where

The value

where

respectively,

In expression (1) values

Spin-dependent transport in systems with strong electronic correlations is described by partial constituent of diagonal conductivity tensor element (1), which corresponds to a specific value of the electron spin projection.

Here are the results of calculation of the energy spectrum of electrons and phonons and conductivity of carbon nanotubes doped with chromium. In calculation, renormalization of vertex parts of mass operator of electron-electron and electron-phonon interactions [

We performed geometry optimization of the crystal structure of carbon nanotube of chirality (3,0) with Cr impurity. Geometric optimization of the crystal structure was achieved by minimizing the free energy. Carbon nanotube doped with Cr has a one-dimensional crystal structure. Primitive cell contains 18 non-equivalent atom positions. Carbon atoms are located in 12 positions on the surface of the inner cylinder. The distance between the carbon atoms is 0.142 nm. Cr atoms are randomly located in the 6 position on the outer surface of the cylinder opposite the center of a hexagon, the vertices of which are carbon atoms. Through the study of free energy minimum found that Cr atoms are randomly located on the surface of nanotubes. This indicates that the probability of Cr atoms arrangement

The value localized magnetic moment projection of the atom Cr and induced localized magnetic moment of an atom C in the direction of the magnetic field increases with the size of the field. For carbon nanotubes of 5 Cr atoms in primitive cell value projection magnetic moment of the atom Cr varies within

of carbon nanotube with an admixture of Cr in the absence of external magnetic field. In the absence of a magnetic field

In

As shown in

In

Thus, the phenomenon of spin-dependent electron transport in a carbon nanotube is the result of strong electron correlations caused by the presence of chromium atoms. The value of the spin polarization of electron transport determined by the difference of the partial densities of states (