Pseudopotential calculations for(GaAs)1-(AlAs)1and related monolayer heterostructures

New atomic pseudopotential form factors are found for Ga, Al, and As. These simultaneously fit the energy bands of pure GaAs and AlAs. With these, eigenvalues and eigenvectors of the ${\mathrm{}\left(\mathrm{GaAs}\right)\mathrm{}}_1$-${\mathrm{}\left(\mathrm{AlAs}\right)\mathrm{}}_1$ monolayer heterostructure are found and the density of states, the dielectric functions, and the charge density are calculated. With the additional assumption of the virtual-crystal approximation, the composition dependence of the principal valence-band maxima and conduction-band minima is found for ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$, ${\left({\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}\right)}_1-{\left({\mathrm{Al}}_{1-x}{\mathrm{Ga}}_x\mathrm{As}\right)}_1$, and ${\left(\mathrm{GaAs}\right)}_1-{\left({\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}\right)}_1$. It is shown that ${\mathrm{}\left(\mathrm{GaAs}\right)\mathrm{}}_1$-${\mathrm{}\left(\mathrm{AlAs}\right)\mathrm{}}_1$ has electronic properties which are quite distinct from GaAs, AlAs, and ${\mathrm{Ga}}_{0.5}$ ${\mathrm{Al}}_{0.5}$As. The effects of disorder on the principal band gaps are discussed. The theoretical results are compared to past experiments and several new experiments are suggested.