In this work, we investigate impurity-induced Friedel oscillations in the doped two-dimensional Hubbard model, focusing on the role of holon and doublon excitations. We show that weak impurities, due to the nonfermionic nature of the underlying quasiparticles, induce Friedel oscillations whose behavior is consistent with an effective noninteracting theory for these quasiparticles and whose wave vector reflects the violation of Luttinger's theorem. At larger impurity strength, the system transitions to a phase-separated state composed of coexisting Mott-insulating (half-filled) and hole-rich regions. Within the composite operator framework, this phase separation arises from a competition between the kinetic energy of holons and the tendency to form tightly bound holon-doublon pairs. Our results offer insights into the nature of charge carriers and the emergent electronic phases in the doped Mott regime.

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• Disordered systems
• Mott insulators
• Hierarchical equations of motion
• Hubbard model