Coherent-potential approximation single-site

In the last years 4-8 mol percent hydrogen impurities have been found in (SN) at IBM, San Jose ( ). One of the most probable site of H bonding is the N atom in the (SN) units. To investigate the effect of randomly distributed H atoms on the band structure of (SN) we have performed a single site one-band coherent potential approximation (CPA) calculation for the (SN)... 

Abe and Toyozawal have shown numerically that this non-universal form can be approximated by a simple exponential for the particular case of Gaussian single site disorder perturbing a semicircular density of states in the Coherent Potential Approximation (CPA). 

SINGLE-SITE COHERENT POTENTIAL APPROXIMATION AND ITS APPLICATION TO (SN) WITH HYDROGEN IMPURITIES... 

The Coherent Potential Approximation (CPA) of the electronic structure of a disordered system is based on the idea that the disordered system should be replaced by an effective medium. This medium has the property that the statistical average of the fluctuation from its potential (the so-called coherent potential) should be equal to zero. In other words, each site but one is replaced by an unknown coherent potential. One then puts at the reference site (see Figure 4.13) an A or a B component (in the simplest case of a binary disordered system) with respective probabilities 1 — /and /. After that one solves the problem of this single impurity imbedded in the effective medium characterized by the coherent potential, which is determined by the requirement that the average scattering (fluctuation) from the reference site is also zero. 

In order to solve the multiple-scattering problem for the alloy, one replaces the original random alloy by an ordered lattice of effective scatterers, or the so-called effective medium. The effective medium is described by a site U (but not a sort i) dependent (complex) coherent potential. Therefore, the eflFective medium has the symmetry of the underlying crystal lattice. In the single site approximation the properties of these effective atoms have to be determined self-consistently by the condition that the scattering of electrons of real atoms embedded in the effective medium vanish on the average. For a disordered binary alloy this idea is schematically illustrated in Fig. 2. 

---