Casimir vacuum energy at angstrom-scale crystal lattice gaps: a multi-oscillator Lifshitz screen of asymmetric layered materials

The Dzyaloshinskii-Lifshitz-Pitaevskii (DLP) Casimir formula is evaluated on the imagi- nary frequency axis using the Rakic 1998 Lorentz-Drude multi-oscillator dielectric func- tion for 26 metals and layered materials at their natural interplanar spacings (1.8 to 7.4 Å). The method is checked for consistency against one published measurement and one independent computational study. For the White et al. 2021 Cu-Cu engineered cavity at 1 µm, the computed energy density |E/A| agrees with the measured power output to within 10% under a single-rate-constant assumption. For the Moddel et al. 2021 Pd/NiO/Ni metal-insulator- metal (MIM) tunnel diode at 33 nm, the finite-plasma Drude shape ex- ponent extracted from the pipeline is α = −2.39, consistent with a realistic dielectric (PC gives α = −3 exactly). The Casimir energy density at angstrom scale is ~4.5×10⁸ times larger than at the White chip’s micrometer gap, after the Cu multi- oscillator di- electric suppression of 0.4% relative to a perfect conductor is applied. An asymmetry figure of merit FOM = |E/A| × asymmetry_fraction × abundance_factor is defined for en- gineered heterocavities and evaluated across 9 candidate platforms. Graphene / lithium- intercalated graphite (LiC₆) is identified as the top abundance-weighted intercalation heterocavity, with FOM = 8.45×10⁻⁴ (eV/Ų), roughly 2.4× the Cu-Au engineered metal heterocavity. A separate class of substitutionally doped commodity transition-metal hosts is then screened by a gap-extreme lattice- distortion model for seven heavy-element dopants (Sn, Sb, Te, Pb, Bi, Tl, Po) in two hosts (Ni and Co), yielding a new leader: Bi-doped Ni (and the degenerate Tl-doped Ni, same atomic radius) at FOM = 6.46×10⁻³ eV/Ų, a factor of 7.64× the graphene/LiC₆ value and produced from commodity materi- als already in industrial circulation. All computed numbers are lower bounds on the total van der Waals interaction: the DLP framework captures the retarded photon-pressure channel but is agnostic to non-retarded dispersion and short-range chemical overlap.