Topologically protected quantum metallic bonding of alkali metals: From entangled electron–phonon dynamics
Bibliographic record
Abstract
We show that metallic bonding in the alkali metals can be recast as a symmetry- and topology-guided electron–phonon problem. Using mode-resolved second derivatives of band energies with respect to normal-mode displacements, we find sharp, equal-and-opposite curvature poles confined to the H → N line of the body-centered cubic Brillouin zone. These poles diagnose interband mixing within a quasi-degenerate doublet and are quantitatively captured by a minimal Dirac/two-level model with a phonon-tunable mass. Independent topology diagnostics reveal odd-parity windings and unit-chirality Weyl charges near H → N, establishing that the symmetry-selected crossings carry quantized Berry curvature. Quantizing the normal-mode coordinate elevates the static picture to a pseudo-spin-boson Hamiltonian; across the series, Li, K, Rb, and Cs lie near the resonance between degeneracy-lifting energies and longitudinal phonon frequencies, while Na is off-resonant, explaining its weaker, parabolic response. The resulting view is that “simple” metallic bonding emerges from selective, longitudinal-mode electron–phonon entanglement localized at symmetry points: phonons open and tune gaps without destroying the underlying linear dispersion. These findings suggest that quantum coherence is not merely preserved in low-dimensional systems or isolated defects but may be intrinsic to certain metallic phases. The results open new avenues for realizing lattice-based quantum sensors, analog quantum simulators, and coherence-driven materials design, embedding quantum functionality directly into the structural foundation of matter.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".