Optical conductivity of ortho-II Y Ba 2 Cu 3 O 6.5

The ortho-II phase of $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.5}$ is characterized by a periodic alternation of empty Cu and filled $\mathrm{Cu}\ensuremath{-}\mathrm{O}$ $b$-axis chains doubling the unit cell in the $a$ direction. The extra oxygen in the full chains gives rise to an attractive potential for the holes in the planes. The planar bands split in two with a gap opening at the new Brillouin zone boundary ${k}_{x}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}∕2$, which we estimate from local-density approximation calculations. Using a planar model which treats the $d$-wave superconductivity in a mean field approximation, we show that interband transitions produce a strongly anisotropic feature in the optical conductivity controlled by a region in $\stackrel{P\vec}{k}$-space close to $(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$. The edge position of this feature gives information on the temperature dependence of quasiparticle spectrum in this region. Bilayer splitting would show up as a double edge shape.