In-plane anisotropy of the electronic structure for the charge/orbital-ordered state in half-doped manganite with layered structure

We report on the in-plane anisotropy of the electronic response in the spin/charge/orbital ordered phase of a half-doped layered-structure manganite. The optical conductivity spectra for a single domain of Eu$_{1/2}$% Ca$_{3/2}$MnO$_{4}$ unambiguously show the anisotropic charge dynamics which well corresponds to the theoretical calculation: the optical conductivity with the polarization along the zigzag ferromagnetic chain direction exhibits a smaller gap and a larger intensity at lower energies than that of the perpendicular polarization mostly due to the charge/orbital ordering and the associated quantum interference effect.