Coherent potential

Polarons of Molecular Crystal Model by Nonlocal Dynamical Coherent Potential Method... 

The present paper is devoted to the theoretical formulation and numerical implementation of the NDCPA. The dynamical CPA is a one-site approximation in which variation of a site local environment (due to the presence, for example, of phonons with dispersion) is ignored. It is known from the coherent potential theory for disordered solids [21], that one can account in some extension the variation of a site local environment through an introduction of a nonlocal cohcn-cnt potential which depends on the difference between site... 

Let us introduce the coherent potential Vk(E) which is thought to be dependent on energy E and exciton momentum k. The coherent potential is translational invariant in the site representation. The Hamiltonian (1) is transformed with the coherent potential taken into account as... 

We restrict ourselves to the case of the system at zero temperature. This is not relevant from the point of view of methodology. The case of nonzero temperatures may be considered in the completely analogous fashion. At zero temperature the coherent potential is chosen so that the Gmi(z) and G /(z) averaged over phonon degrees of freedom in phonon vacuum are equal... 

This is the operator (or matrix) equation for the coherent potential v(z). The formal expression for v(z) can be easily written. The exciton polaron is... 

Let us first consider a case of the polaron spectrum when condition (20) is fulfilled so that the nondiagonal matrix elements of the operator F can be neglected, we denote as Vinei the coherent potential in which only the inelastic scatterings are accounted. It is easy show by explicit calculations that... 

Using Eqs. (29) and (30) we obtain that the coherent potential v i with elastic scattering correction is determined by the following equations... 

We have used the multisublattice generalization of the coherent potential approximation (CPA) in conjunction with the Linear-MufRn-Tin-Orbital (LMTO) method in the atomic sphere approximation (ASA). The LMTO-ASA is based on the work of Andersen and co-workers and the combined technique allows us to treat all phases on equal footing. To treat itinerant magnetism we have employed for the local spin density approximation (LSDA) the Vosko-Wilk-Nusair parameterization". 

Figure 2.Virtual crystal approximation calculations (solid line) compared with coherent potential approximation calculations for Fe-Co (longdashed line), Fe-Ni (dot-dashed line) and Fe-Cu (dashed line). The fcc-bcc energy difference is shown as a function of the atomic number.

I.A. Abrikosov and H.L.Skriver, Self-consistent linear-muffin-tin-orbitals coherent-potential technique for bulk and surfaces calculations Cu-Ni, Ag-Pd, and Au-Pt random alloys, Phys. Rev. B 47, 16 532 (1993). 

It would be interesting to compare these results with those of a CPA (coherent potential approximation) calculation. For a real test of both methods a system should be found which shows a more pronounced change when going from one phase to the other, than found for the system presented in this paper. 

Application of the Coherent Potential Approximation (CPA) alloy theory in connec-... 

Ffom a theoretical point of view, stacking fault energies in metals have been reliably calculated from first-principles with different electronic structure methods [4, 5, 6]. For random alloys, the Layer Korringa Kohn Rostoker method in combination with the coherent potential approximation [7] (LKKR-CPA), was shown to be reliable in the prediction of SFE in fcc-based solid solution [8, 9]. 

P.A.Korzhavhi, A.V.Ruban, I.A.Abrikosov and H.L.Skriver, Madelung energy for random metallic alloys in the coherent potential approximation , Phys. Rev. B51 5773 (1995) ... 

The improvement came in the form of the coherent-potential approximation (CPA) (Soven 1967, Taylor 1967, Velicky et al 1968), which remedied the lack of self-consistency exhibited by the ATA. The crux of this approach is that each lattice site has associated with it a complex self-consistent potential, called a coherent potential (CP). The CP gives rise to an effective medium with the important property that removing that part of the medium belonging to a particular site, and replacing it by the true potential, produces, on average, no further scattering. Because the CPA is used for our discussion of chemisorption on DBA s, its mathematical formulation is given below. 

---