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

It is important for modern scanning microwave microscopes to overcome the effect of the surface roughness. Here, we report microwave conductivity imaging of 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 distinguished from topography-induced contrast using a combination of a scanning tunneling microscope and a scanning microwave microscope (STM-SMM). We observed the characteristic modulation of the local electric property that originates from the mesoscopic phase separation of the metallic and semiconducting phases in two different scanning modes: constant current (CC) mode and constant $Q$ (CQ) mode. In particular, CQ scanning is useful because we obtain a qualitative image in which the topographic contrast is largely eliminated without degradation of the spatial resolution.