Electrodynamics of Lattice Vacuum Defects: The Topological Origin of Drift-Induced Hole Generation

Abstract

Electrodynamics of Lattice Vacuum Defects: The Topological Origin of Drift-Induced Hole Generation Abstract & Main Contents This manuscript presents a topological vacuum-defect model of solid-state hole mechanics, providing a deterministic physical explanation for effective mass, hole mobility, and dynamic carrier generation in crystalline solids. Rather than treating the hole as an abstract, mathematical quasiparticle near the top of a valence band, this work demonstrates that a solid-state hole is the lattice-constrained counterpart of a free-space positron: a real, topologically folded vacuum defect. The manuscript establishes several key physical mechanisms, derivations, and experimental protocols: Spatial Origin of Variable Hole Mass (mh* ∝ 1/ratomn): Demonstrates that nuclear pre-stress creates a radial vacuum-stiffness gradient inside unit cells. Compact atomic cores produce high local stiffness and heavy effective masses, whereas larger atomic radii spread the topological fold across a greater volume, yielding lighter measured hole masses. This relation is validated against measured heavy- and light-hole masses in Group IV semiconductors (Si, Ge, α-Sn) and Group 11 metals (Cu, Ag). Asymmetric Mechanics & Topological Convolution: Explains why holes exhibit high mobility despite being localized defects. Unlike valence electrons undergoing rigid Newtonian acceleration (F=qE) against scattering centers, an induced topological vacuum fold possesses structural elasticity, allowing it to convolve and self-adjust to local unit-cell geometry. Resolution of the Alkali Metal Paradox: Uses orbital boundary symmetry to explain why ns1 alkali metals display strictly single-carrier (electron) transport. Isotropic, spherical s-shells lack directional boundary seams to anchor positive-induction folds, whereas directional covalent/transition-metal bonding supplies the necessary boundary asymmetry. Dynamic Hole Generation via Trailing Wakes (nhdyn = α·ne·(ℓ/a)): Reveals that under non-equilibrium drift where carrier mean free paths span tens to hundreds of unit cells (l/a ≫ 1), a drifting electron leaves a trailing wake of uncompensated positive topological vacancies. High-Frequency Phase Lag & Wake Collapse: Shows that at high frequencies (ωτᵣ ≫ 1), the drive field alternates faster than a wake can form, causing the dynamic hole contribution to collapse toward a purely electronic Hall response. Testable Experimental Protocols: Proposes three concrete laboratory tests to validate the framework: Sub-terahertz Hall effect spectroscopy to detect the phase shift and collapse of the dynamic wake. Low-temperature cyclotron resonance on gray tin (α-Sn) to observe ultra-light hole masses (mlh*/m0 < 0.02). Mean-free-path tuning (l/a) in disordered binary alloys to measure wake suppression. Integration & Connection to Previous Published Works This manuscript extends a single, continuous research program examining classical vacuum topology across particle physics, atomic architecture, electrodynamics, and solid-state transport: Sub-Cycle Electrodynamics & Energy Transport: (Ref. [4] in manuscript: "Phase-Resolved Analysis of Electromagnetic Energy Transport via the Instantaneous Poynting Vector", ECSarXiv/OSF, 2026) Connection: Uses the 2ω frequency-doubling identity and phase-resolved sub-cycle energy relay mechanism of the instantaneous Poynting vector S = E × H. This sub-cycle phase logic directly underpins both the energy pulse required for vacuum rupture and the high-frequency relaxation phase lag (ωτᵣ) of dynamic hole wakes. Free-Space Pair Production & Topological Vacuum Mechanics: (Ref. [3] in manuscript: "Structural Mechanics in Vacuum Electrodynamics: A Classical Topological Approach", Zenodo, 2026) Connection: Extends the classical chiral-folding mechanism—where electrons and positrons emerge as topological solitons near a gravitational anvil—into the crystalline lattice. The solid-state hole is derived as the spatially constrained analogue of the free-space positron. Empirical Physical Periodic System: (Ref. [5] in manuscript: "Reconstructing the periodic table using the physical parameters of nuclear architecture", Research Square, 2026) Connection: Employs the empirical atomic radii (ratom) and nuclear architecture dataset tabulated across all 118 elements in the reconstructed 15-period matrix as the quantitative baseline for local unit-cell volume and vacuum-stiffness derivations. Dual-Axis & Hierarchical Atomic Models: (Ref. [6] & [7] in manuscript: "Derivation of a Dual-Axis Model..." and "Recurring Periodic Relationships and Hierarchical Organization...", Zenodo / Preprints, 2026) Connection: Applies the two-center (Lp/Rp) dual-axis asymmetric core geometry and hierarchical support-level structures to define the directional boundary seams necessary for anchoring localized positive-induction defects in crystals.