Metallic bonding in close packed structures: structural frustration from a hidden gauge symmetry

TL;DR

This paper reveals a hidden gauge symmetry in close-packed alkali metals like lithium and sodium, explaining their structural complexity and degeneracy, and how subtle effects break this symmetry to select specific structures.

Contribution

It introduces a gauge symmetry framework that predicts identical electronic structures for all close-packed configurations in Li and Na, offering a new explanation for their structural behavior.

Findings

Gauge symmetry enforces degeneracy of close-packed structures.

Weak effects can break the symmetry and select specific structures.

The framework may explain phase transitions in alkali metals.

Abstract

Based on its simple valence electron configuration, we may expect lithium to have straightforward physical properties that are easily explained. However, solid lithium, when cooled below 77 K, develops a complex structure that has been debated for decades. A close parallel is found in sodium below 36 K where the crystal structure still remains unresolved. In this letter, we explore a possible driving force behind this complexity. We begin with the observation that Li and Na form close-packed structures at low temperatures. We demonstrate a gauge symmetry that forces \textit{all} close-packed structures to have the same electronic energy and, in fact, the very same band structure. This symmetry requires two conditions: (a) bands must arise from $s$ orbitals, and (b) hoppings beyond second-nearest neighbours must be negligible. We argue that both can be reasonably invoked in Li and Na. When these conditions are satisfied, we have extensive degeneracy with the number of competing iso-energetic structures growing exponentially with linear system size. Weak effects, such as $p$-orbital admixture, long-range hopping and phonon zero-point energy, can break this symmetry. These can play a decisive role in `selecting' one particular ordered structure. This point of view may explain the occurrence of ordered structures in Li and Na under pressure. Our results suggest that martensitic transitions may also occur in heavier alkali metals such as potassium.