Doping Dependence of Two Energy Scales in the Tunneling Spectra of Superconducting La${}_{2-x}$Sr${}_x$CuO${}_4$

Scanning tunneling microscopy and spectroscopy have been performed on superconducting La${}_{2-x}$Sr${}_x$CuO${}_4$ ($x=0.06,0.12,0.16$, and 0.21) at 4.2 K. Atomically resolved surface topography has been observed on the $ab$ surface, which exhibits a one-dimensional structure corresponding to the buckling pattern of the orthorhombic phase. The tunneling spectra of all samples exhibit kinks at about $\pm 5$ meV in addition to the energy gap, indicating the existence of two energy scales. While the gap magnitude varies on the length scale of a few nm and steadily increases upon underdoping, the kink energy is spatially uniform on the surface and almost independent of the doping level.