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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 teacher head, 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".