Low-energy electronic state of the structural modulation-free Bi₂ Sr₂ CuO_{6 + δ} studied by the scanning tunneling microscopy

We report scanning tunneling microscopy (STM) studies on the structural modulation-free Bi₂ Sr₂ CuO_{6 + δ} in which Bi atoms are partially substituted by Pb atoms. Optimally doped sample with the superconducting transition temperature T_c = 22 K shows short atom-strings at a bias-voltage of 5 mV. Some strings are bundled and aligned along the orthogonal oriented two Cu-O-Cu directions randomly. Atom-strings are also observed in the overdoped sample (T_c = 7 K), while they are hardly seen in the heavily overdoped sample (T_c = 4.5 K). It is found that the disturbance from overdoped holes reduces the number of atom-strings and obscures every atom-string. These results indicate that the CuO₂ plane possesses not only the two-dimensional electronic correlation caused by the two-dimensionality but also short-range one-dimensional one.