We discuss the electronic structure of the first four members of the high-$T_c$ superconductor family ${\mathrm{Tl}}_2{\mathrm{Ba}}_2{\mathrm{Ca}}_{L-1\mathrm{}}{\mathrm{Cu}}_L{\mathrm{O}}_{4+2L}$, where $L$ is the number of Cu${\mathrm{O}}_2$ layers. Using a simplified BCS-type model, we relate $T_c$ to $L$ using the partial density of states of the Cu${\mathrm{O}}_2$ layers as the physical link. According to our model, the pure phase of ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_3$ ${\mathrm{Cu}}_4$${\mathrm{O}}_{12}$ ($L=4\mathrm{}$) would have a value of $T_c$ in the range 135 to 165 K.

• Received 2 May 1988

DOI:https://doi.org/10.1103/PhysRevB.38.6470