Visualizing electronic segregation in lightly-doped Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$

We report spectroscopic imaging on evolution of the electronic state in a lightly-doped cuprate superconductor Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$ across the metal-insulator critical doping. We find nm-scale electronic segregation between regions breaking and showing the lattice symmetry. The former shows C$_2$ symmetry characterized by the unidirectional nano-domains and the V-shaped pseudogap found in superconducting samples [1] while the latter shows C$_4$ symmetry and wider U-shaped gap prominent in non-superconducting samples. This indicates that the local symmetry breaking is inherent in the electronic states created inside the Mott gap by hole doping. We also discuss spectra in C$_2$/C$_4$ domains and superconducting/insulating samples. \par ~ \par \noindent [1] Y. Kohsaka et al., Science 315, 1380 (2007), Nature 454, 1072 (2008).