Nanoscale Electronic Phase Separation Driven by Fe-site Ordering in Fe\textsubscript{5-x}GeTe\textsubscript{2}

Abstract: Understanding how local structural order governs electronic correlations is essential for revealing the microscopic mechanism underlying emergent behavior in two-dimensional magnets. In the layered van der Waals ferromagnet Fe\textsubscript{5-x}GeTe\textsubscript{2}, intrinsic Fe-site disorder provides a natural platform to probe this interplay. Here, we establish a direct atomic scale correlation between Fe-site ordering and local electronic structure by combining high-resolution scanning tunneling microscopy with density functional theory calculations. Scanning tunneling microscopy resolves two coexisting surface phases, a $\sqrt{3} \times \sqrt{3}$ superstructure associated with ordered Fe(1) configurations and an undistorted $1 \times 1$ hexagonal Te lattice in Fe(1)-deficient regions. Spatially resolved spectroscopy shows that the $\sqrt{3}$-ordered domains exhibit metallic behavior, whereas Fe(1) vacant areas display a suppressed density of states(DOS) near the Fermi level, indicative of pseudogapped electronic states. The nanoscale coexistence of these distinct electronic responses provides direct evidence of electronic phase separation driven by Fe-site ordering. First-principles calculations reveal that symmetry allowed hybridization between Fe 3d and Te 5p orbitals reconstructs the low-energy electronic structure, giving rise to the contrasting tunneling signatures of ordered and disordered phases. Bias-dependent local DOS simulations reproduce the experimentally observed contrast evolution and reveal that hybridization induced out of plane orbital character governs the spatial modulation of tunneling conductance. These results provide a microscopic framework linking atomic-scale structural order to nanoscale electronic inhomogeneity in van der Waals magnets.