Topologically protected quantum metallic bonding of alkali metals: From entangled electron–phonon dynamics

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.