Mineral Björn Hoiland

Vacuum Forge Labs•Quantum/Theoretical Physics Solutions

QVC Multilayer Simulator

Topological & Quantum Vacuum Properties of Twisted Multilayers

This interactive mathematical simulator explores the topological and quantum vacuum properties of twisted multilayer heterostructures relevant to Quantum Vacuum Catalyzation theory. Navigate between five analysis modules using the tabs below.

QVC research simulator v0.3 — multilayer topological engine
Chern numbers · flat bands · Berry curvature · multilayer graphene QVC
Odd Chern invariants, moiré magic-angle flat bands, and topological vacuum catalyzation — from monolayer to pentalayer ABC heterostructures. All parameters interactive.

ABC (rhombohedral) N-layer stacking gives C = N per layer. Pentalayer: C = 5 (odd). Bandwidth W_N = γ₁·(γ₁/γ₀)^(N−1) collapses exponentially — W₅ ≈ 79 μeV. Odd Chern numbers carry Z (integer) topological protection, stronger than Z₂ invariants.

Stacking:
Max layers5
Displacement field D0.60 × D₀
N=1 C=1
381.00 meV
κ 8.6% · odd Z
N=2 C=2
45.94 meV
κ 52.7%
N=3 C=3
5.54 meV
κ 99.8% · odd Z
N=4 C=4
667.80 μeV
κ 100.0%
N=5 C=5
80.50 μeV
κ 100.0% · odd Z
Chern number per N — purple = odd C (Z invariant), teal = even C (Z₂)
Bandwidth W_N (log, amber) and QVC catalyzation κ (purple dashed) vs layers
Pentalayer ABC: W ≈ 79 μeV → κ_QVC → 0.999. C=5 (odd) → Z topological invariant — Hopfion Q_H adds coherently.
Physics basis: ABC W_N=γ₁(γ₁/γ₀)^(N−1) exact · BM α-parameter exact · Berry curvature 2-band Lorentzian model · σ_xy=C·e²/h Chern-Simons quantized · Schwinger n=1 leading term · VK bound |Q|^(3/4) · κ_total uses independent-factor product formula · QVC parameters (θ_CS, κ_Berry coupling constant) are phenomenological — their derivation from the catalyzation Lagrangian is the central open problem.

Analysis Modules

| Tab | Description | |-----|-------------| | Chern Landscape | Topological phase diagram showing Chern number transitions as a function of twist angle and interlayer coupling | | Flat Band / Magic Angle | Bandwidth collapse near magic angles, revealing flat-band conditions critical for correlated states | | Berry Curvature BZ | Brillouin zone heatmap of Berry curvature distribution, highlighting hotspots at K/K' points | | Hall + Schwinger | Quantized Hall conductance plateaus alongside Schwinger pair-production thresholds | | QVC Synthesis | Unified view combining topological invariants, vacuum energy density, and catalyzation metrics |

Physical Motivation

Twisted multilayer systems exhibit remarkable emergent phenomena at magic angles where bands flatten, enhancing electron-electron correlations. In the QVC framework, these flat-band conditions create regions where the effective vacuum structure is dramatically modified: