Nanoscale electronic inhomogeneity in optimally doped single-layer ${\mathrm{Bi}}_2{\mathrm{Sr}}_{1.6}{L}_{0.4}\mathrm{Cu}{\mathrm{O}}_{6+\delta }$, ($L$-Bi2201, $L=\mathrm{La}$ and Gd) as well as bilayer ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212), superconductors has been investigated by the low-temperature scanning-tunneling-microscopy and spectroscopy. The inhomogeneous gap structures are observed above and below $T_c$ on Gd-Bi2201. Increasing the out-of-plane disorder which is controlled by mismatch of the ionic radius between Sr and Ln results in the enhancement of pseudogap region with suppressed coherence peaks in the conductance spectrum, making the gap average larger and the gap distribution wider. The degree of electronic inhomogeneity measured by the distribution width of the gap amplitude is shown to have a correlation with $T_c$ in optimally doped Bi2201 and Bi2212.

• Received 18 November 2005

DOI:https://doi.org/10.1103/PhysRevB.74.094503