Dopant-Induced Nanoscale Electronic Inhomogeneity in Ca2-xSrxRuO4

Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ single crystals with 0.1 $\le \quad x \quad \le $ 2.0 have been studied systematically using scanning tunneling microscopy (STM) and spectroscopy (STS), low-energy electron diffraction (LEED), and angle resolved photoelectron spectroscopy (ARPES). In contrast to the well-ordered lattice structure, the local density of states (LDOS) at the surface clearly shows a strong doping dependent nanoscale electronic inhomogeneity, regardless of the fact of \textit{isovalent }substitution. Remarkably, the surface electronic roughness measured by STM and the inverse spectral weight of quasiparticle (QP) states determined by ARPES are found to vary with $x$ in the same manner as the bulk in-plane residual resistivity, following the Nordheim rule. For the first time, the surface measurements--especially those with STM--are shown to be in good agreement with the bulk transport results, all clearly indicating a doping induced electronic disorder in the system.