Electronic Crystal State in a Hole Doped Cuprate

In cuprate superconductors, there are four ground states depending on the doping level namely undoped Mott insulator, pseudogap phase, superconductor, and normal metal. Among these phases, the pseudogap phase in the lightly doped regime is rich in peculiar phenomena which may be closely related to the strong correlation effects in cuprates. We have carried out scanning tunneling microscopy/spectroscopy (STM/STS) on Ca$_{2-x} $Na$_x$CuO$_2$Cl$_2$ single crystals ($x=0.08\sim0.12$) to visualize the spatial variation of the electronic states in the pseudogap phase. This compound has a simple crystal structure with only one crystallographic Cu site and provides high quality cleaved surfaces of lightly doped regime. We found 'checkerboard' local density of states (LDOS) modulation which is characterized by the tiling of the commensurate $4a \times 4a$ electronic entity. Each $4a \times 4a$ unit cell carries intricate internal structures which include $4a/3 \times4a/3$ LDOS modulation. The modulation amplitudes of these components are strongly energy dependent but the periodicities are energy independent, both inside and outside of the pseudogap. This suggests that the pseudogap phase is associated with the electronic order or electronic crystal which manifests itself as the observed `checkerboard'. \\ Reference: T. Hanaguri {\it et al.}, Nature {\bf 430}, 1001 (2004).