Advanced synchrotron radiation focusing down to a size of 300 nm has been used to visualize nanoscale phase separation in the K${}_{0.8}$Fe${}_{1.6}$Se${}_2$ superconducting system using scanning nanofocus single-crystal x-ray diffraction. The results show an intrinsic phase separation in K${}_{0.8}$Fe${}_{1.6}$Se${}_2$ single crystals at $T$ < 520 K, revealing the coexistence of (i) a magnetic phase characterized by an expanded lattice with superstructures due to Fe vacancy ordering and (ii) a nonmagnetic phase with an in-plane compressed lattice. The spatial distribution of the two phases at 300 K shows a frustrated or arrested nature of the phase separation. The space-resolved imaging of the phase separation permitted us to provide direct evidence of nanophase domains smaller than 300 nm and different micrometer-sized regions with percolating magnetic or nonmagnetic domains forming a multiscale complex network of the two phases.

The complex electronic properties of ${\mathrm{ZrTe}}_5$ have recently stimulated in-depth investigations that assigned this material to either a topological insulator or a 3D Dirac semimetal phase. Here we report a comprehensive experimental and theoretical study of both electronic and structural properties of ${\mathrm{ZrTe}}_5$, revealing that the bulk material is a strong topological insulator (STI). By means of angle-resolved photoelectron spectroscopy, we identify at the top of the valence band both a surface and a bulk state. The dispersion of these bands is well captured by ab initio calculations for the STI case, for the specific interlayer distance measured in our x-ray diffraction study. Furthermore, these findings are supported by scanning tunneling spectroscopy revealing the metallic character of the sample surface, thus confirming the strong topological nature of ${\mathrm{ZrTe}}_5$.