Metallic Bonding in Close-Packed Structures: Structural Frustration from a Hidden Gauge Symmetry.

Area of Science:

• Solid-state physics
• Materials science
• Quantum mechanics

Background:

• Lithium (Li) and sodium (Na) exhibit complex crystal structures at low temperatures, defying simple predictions based on their electronic configurations.
• The precise crystal structures of solid Li below 77 K and Na below 36 K remain unresolved and debated.
• These alkali metals form close-packed structures under specific conditions.

Purpose of the Study:

• To investigate the driving force behind the complex low-temperature crystal structures of lithium and sodium.
• To explore the role of electronic band structure and symmetry in determining structural complexity.
• To provide a theoretical framework for understanding the emergence of ordered structures in alkali metals.

Main Methods:

• Demonstration of a gauge symmetry applicable to close-packed structures.
• Analysis of electronic energy and band structure under symmetry conditions.
• Consideration of symmetry-breaking effects like p-orbital admixture and long-range hopping.

Main Results:

• A gauge symmetry dictates that all close-packed structures, under specific conditions (s-orbital bands, limited hopping), possess identical electronic energy and band structure.
• This symmetry leads to extensive degeneracy, with the number of isoenergetic structures growing exponentially with system size.
• Weak perturbations, including p-orbital admixture and phonon effects, can break this symmetry and select specific ordered structures.

Conclusions:

• The observed structural complexity in Li and Na arises from a high degree of electronic degeneracy driven by a gauge symmetry.
• Symmetry-breaking effects are crucial in selecting the final ordered structure observed in experiments.
• The theoretical framework suggests that similar phenomena, potentially leading to martensitic transitions, may occur in heavier alkali metals like potassium (K).