On the Electronic Contribution to Crystalline Diffraction Patterns

Abstract: We introduce the electronic structure factor as a phase-sensitive contribution to diffraction that directly encodes the properties of the occupied-band wave functions. In the one-dimensional SSH model, $F_{\mathrm{cond}}$ is governed by the relative sublattice phase, which integrates to the Zak phase. This provides a clear diffraction-based criterion to distinguish trivial and topological regimes in the absence of any structural change. Beyond the SSH limit, the same Bloch-based construction naturally accounts for commensurate and incommensurate magnetic satellites in antiferromagnets, reproducing the additional peaks at $q=G\pm Q$ observed in NiO, MnO, chromium, and cuprates. These results demonstrate that diffraction can probe electronic topology and magnetic ordering on equal footing, opening a route to phase-sensitive structural characterization of correlated electron systems.