Inverse design for Casimir-Lifshitz force near heterogeneous gapped metal surface

The Casimir-Lifshitz force is calculated between a heterogeneous gapped metal surface and a silica sphere attached to an AFM cantilever tip. We demonstrate that heterogeneous surface patches with different off-stoichiometry surface properties lead to changes in the predicted distances for a specific force. This can incorrectly be interpreted as occurrences of surface roughness.

💡 Research Summary

The manuscript presents a comprehensive theoretical study of Casimir‑Lifshitz forces acting between a heterogeneous “gapped‑metal” surface and a sphere (either silica or gold) attached to an atomic‑force‑microscope (AFM) cantilever. Gapped metals are a class of materials that simultaneously exhibit metallic free‑carrier response and an electronic band gap; their dielectric response can be tuned by altering stoichiometry, which in turn changes the concentration of intrinsic defects such as cation vacancies. The authors focus on two families of such materials—Ba₁₋ₓNb₁₋ᵧO₃ (five compositions) and Ca₆₋ₓAl₇O₁₆ (three compositions)—and compute their electronic structures using density‑functional theory (DFT) with the PBE functional and a Hubbard‑U correction (U = 1.5 eV for Nb d‑states). Both Drude free‑carrier contributions and interband transitions are included; a small Lorentzian broadening (0.01 eV) is applied in the Kramers‑Kronig transformation to obtain reliable imaginary‑frequency dielectric functions ε(iξ).

The calculated ε(iξ) curves show a strong dependence on off‑stoichiometry: as Nb or Al vacancies increase, the Drude term is suppressed and the material evolves from metallic‑like to insulating‑like behavior. To make the data usable in Lifshitz‑type force calculations, the authors fit each dielectric function to a 13‑oscillator model ε(iξ)=1+∑ₖ Cₖ/