Electronic structure of ladder cuprates

We study the electronic structure of the ladder compounds $\mathrm{Sr}{\mathrm{Cu}}_2{\mathrm{O}}_3$ and ${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}.$ Our local-density approximation calculations for $\mathrm{Sr}{\mathrm{Cu}}_2{\mathrm{O}}_3$ give similar Cu $3d$ bands near the Fermi energy as reported for ${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}.$ The hopping parameters estimated by fitting these bands show a strong anisotropy between the $t_{\perp }$ and $t_{\Vert }$ intraladder hopping and small interladder hopping. A downfolding method shows that this anisotropy arises from the ladder structure. The conductivity perpendicular to the ladders is computed assuming incoherent tunneling giving a value close to experiment.