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Direct observation of nanoscale interface phase in the superconducting chalcogenide K$_{x}$Fe$_{2-y}$Se$_2$ with intrinsic phase separation

We have used scanning micro x-ray diffraction to characterize different phases in superconducting K$_{x}$Fe$_{2-y}$Se$_2$ as a function of temperature, unveiling the thermal evolution across the superconducting transition temperature (T$_c\sim$32 K), phase separation temperature (T$_{ps}\sim$520 K) and iron-vacancy order temperature (T$_{vo}\sim$580 K). In addition to the iron-vacancy ordered tetragonal magnetic phase and orthorhombic metallic minority filamentary phase, we have found a clear evidence of the interface phase with tetragonal symmetry. The metallic phase is surrounded by this interface phase below $\sim$300 K, and is embedded in the insulating texture. The spatial distribution of coexisting phases as a function of temperature provides a clear evidence of the formation of protected metallic percolative paths in the majority texture with large magnetic moment, required for the electronic coherence for the superconductivity. Furthermore, a clear reorganization of iron-vacancy order around the T$_{ps}$ and T$_c$ is found with the interface phase being mostly associated with a different iron-vacancy configuration, that may be important for protecting the percolative superconductivity in K$_{x}$Fe$_{2-y}$Se$_2$.