Calculations of the Electronic Structure of ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x\mathrm{Cu}{\mathrm{O}}_{4-y}$ by the Coherent-Potential Approximation

We present the first calculations of the electronic structure of the high-temperature superconductors in the disordered phase using the tight-binding coherent-potential approximation. These calculations are used to assess the influence of increasing oxygen vacancies when La is alloyed with $M$ (=Sr or Ba) in the system ${\mathrm{La}}_{2-x}{M}_x\mathrm{Cu}{\mathrm{O}}_{4-y}$. Contrary to simple doping arguments, it is found that deoxygenation does not raise the Fermi level ($E_F$). The increase in $T_c$ in the range $0.05<x<\mathrm{}0.15\mathrm{}$ and the decrease in $T_c$ beyond the peak at $x=0.15\mathrm{}$ follow the density of states at $E_F$.