Unconventional incommensurate epitaxy of superconducting FeSe films on SrTiO$_3$
We present a combined X-ray diffraction and transmission electron microscopy study of superconducting FeSe/FeTe multilayers grown by molecular beam epitaxy on SrTiO$_3$(001) substrates. While X-ray diffraction confirms perfect in-plane epitaxial alignment between FeSe, FeTe, and the substrate, scanning transmission electron microscopy reveals a surprising lack of atomic registry at the FeSe/SrTiO$_3$ interface. Instead of adapting to the substrate lattice, FeSe retains its own in-plane lattice spacing. A periodic lateral shift between the atomic positions of FeSe and SrTiO$_3$ is observed, with a registry recurrence length that matches the lattice mismatch determined by X-ray diffraction. No misfit dislocations or other relaxation features are detected at the interface. This coexistence of directional alignment and registry-free growth suggests an unconventional regime of epitaxy in which crystallographic orientation is maintained without atomic matching. The findings offer insight into strain accommodation in layered systems and may have implications for interface engineering in Fe-based superconductors.