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

Abstract

Traditional solid-state physics treats the hole as a mathematical abstraction—a vacant state at the top of a valence band assigned an effective mass mh* purely to balance transport equations—without offering a physical mechanism for why this mass spans more than an order of magnitude across elemental lattices. Extending a classical topological model of pair production—where electrons and positrons arise as chirally folded discontinuities within a pre-stressed vacuum [3,4]—this work projects that framework into crystalline solids. We propose that the solid-state hole is the lattice-confined analogue of the free-space positron: a physical, topologically folded vacuum defect rather than a virtual quasiparticle. Because heavy atomic nuclei act as gravitational anchors that pre-stress the nearby vacuum [3], the volume available for folding at any lattice site is dictated by the empirical atomic radius ratom, a property previously mapped across all 118 elements in a reconstructed periodic system [5]. This gives rise to a radial vacuum-stiffness relation mh* ∝ 1/(ratomn) (where n ≈ 1–2, depending on crystal symmetry and packing fraction), which we benchmark against measured heavy- and light-hole masses in silicon, germanium, and gray tin, as well as Group 11 conductors (copper and silver). Furthermore, we resolve the single-carrier paradox of ns1 alkali metals using orbital geometry: the isotropic, dumbbell-free s-shells described in our dual-axis model [6] lack a boundary seam capable of anchoring a positive-induction defect, whereas the directional Lp/Rp bonding asymmetry in covalent and transition-metal lattices [6,7] naturally provides one. Under non-equilibrium drift, where carrier mean free paths extend across dozens to hundreds of unit cells (ℓ/a ≫ 1), a drifting electron leaves behind a trailing wake of uncompensated topological vacancies, establishing a dynamic hole population nhdyn ∝ ℓ/a. Unlike valence electrons subject to rigid linear acceleration, the induced hole exhibits spatial elasticity, allowing it to convolve around local unit-cell geometry. Finally, we propose three experimental tests—sub-terahertz Hall spectroscopy, low-temperature cyclotron resonance in gray tin, and mean-free-path tuning in disordered alloys—to empirically evaluate this topological defect model against standard quasiparticle theory.