Driven by interactions due to the charge, spin, orbital, and lattice degrees of freedom, nanoscale inhomogeneity has emerged as a new theme for materials with novel properties near multiphase boundaries. As vividly demonstrated in complex metal oxides 1-5 and chalcogenides 6,7 , these microscopic phases are of great scientific and technological importance for research in hightemperature superconductors 1,2 , colossal magnetoresistance effect 4 , phase-change memories 5,6 , and domain switching operations [7][8][9] . Direct imaging on dielectric properties of these local phases, however, presents a big challenge for existing scanning probe techniques. Here, we report the observation of electronic inhomogeneity in indium selenide (In 2 Se 3 ) nanoribbons 10 by near-field scanning microwave impedance microscopy [11][12][13] . Multiple phases with local resistivity spanning six orders of magnitude are identified as the coexistence of superlattice, simple hexagonal lattice and amorphous structures with ~100nm inhomogeneous length scale, consistent with high-resolution transmission electron microscope studies. The atomic-force-microscope-compatible microwave probe is able to perform quantitative sub-surface electronic study in a noninvasive manner. Finally, the phase change memory function in In 2 Se 3 nanoribbon devices can be locally recorded with big signal of opposite signs.
2While the conventional wisdom on solids largely results from the real-space periodic structures and k-space band theories 14 , recent advances in physics have shown clear evidence that microscopic inhomogeneity, manifested as sub-micron spatial variations of the material properties, could indeed occur under certain conditions. Utilizing various probe-sample coupling mechanisms 15 , spatial inhomogeneity has been observed as nanometer gap variations in high-Tc superconductors 1,2 , coexisting electronic states in VO 2 near the metal-insulator transition 3 , ferromagnetic domains in manganites showing colossal magnetoresistance effect 4 , and in an ever-growing list. Probing these non-uniform phases provides not only much knowledge of the underlying interactions, but also valuable information for applications of the domain structures. In particular, spatially resolved properties are of significant interest for phase change and other switching materials to be on board the nanoelectric era [5][6][7][8][9] .While a number of contrast mechanisms 15 have been employed to visualize the electronic inhomogeneity, established scanning probe techniques do not directly access the low-frequency (f) complex permittivity ε(ω) = ε′ + iσ/ω, where ε′ is the dielectric constant and σ the conductivity, which holds a special position to study the ground state properties of materials. For local electrodynamic response, near-field technique is imperative to resolve spatial variations at length scales well below the radiation wavelength 16 . For this study, the working frequency is set at ~1GHz, i.e., in the microwave regime, to stay below resonant excitation...