Coherent-Potential Approximation in a Two-Band Model: Electronic and Transport Properties of Semiconducting Binary Alloys

The formalism of the coherent-potential approximation is extended to include the two-band case. The single-site energy of the one-band case is replaced by a 2 × 2 matrix which varies randomly from site to site according to the occupancy of the site. The Kubo formulas for transport are also extended for the two-band model giving a nonvanishing vertex correction as opposed to the zero vertex correction for the single-band model. The cases treated explicitly correspond to fully disordered binary semiconducting alloys. The band gap and bandwidths are chosen as representative of typical semiconductor values, and concentrations, band gaps, gap centers, and band mixing are all varied systematically. Results are reported for densities of states, parentage, dc conductivity, and the imaginary part of the dielectric constant ${\epsilon }_2\left(\omega \right)$. The analytic behavior of ${\epsilon }_2\left(\omega \right)$ near threshold corresponds to several experimental situations.