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It is important for modern scanning microwave microscopes to overcome theeffect of the surface roughness. Here, we report microwave conductivity imagingof the phase-separated iron chalcogenide K$_x$Fe$_y$Se$_2$ ($x=0.8$,$y=1.6$-$2$), in which electric conductivity-induced contrast is distinguishedfrom topography-induced contrast using a combination of a scanning tunnelingmicroscope and a scanning microwave microscope (STM-SMM). We observed thecharacteristic modulation of the local electric property that originates fromthe mesoscopic phase separation of the metallic and semiconducting phases intwo different scanning modes: constant current (CC) mode and constant $Q$ (CQ)mode. In particular, CQ scanning is useful because we obtain a qualitativeimage in which the topographic contrast is largely eliminated withoutdegradation of the spatial resolution.

Near-field microwave imaging of inhomogeneous K$_x$Fe$_y$Se$_2$: separation of topographic and electric features