Electronic structure of ${\mathrm{HgBa}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_8$: The role of mercury

Local-density-approximation calculations are used to elucidate the electronic structure of ${\mathrm{HgBa}}_2$ ${\mathrm{Ca}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_8$. Unlike the case in the corresponding single-${\mathrm{CuO}}_2$-layer material, there is a Hg-derived band that dips below the Fermi energy, and this hole dopes the cuprate planes. This difference is related to apparent electronegativity differences of one-, two-, and three-layer stacks of ${\mathrm{CuO}}_2$ planes.