Empilement aléatoire et frustration - Ganesh Ramachandran (Brock U)

Stacking with randomness and frustration: the curious case of lithium and sodium

Close-packing of spheres is a beautiful mathematical problem with a long, colourful history that spans centuries. To achieve maximal density, we must first arrange spheres into triangular layers and stack them. This is best seen in the crystal structures of elemental solids, with more than half of all elements being close-packed. Lithium and sodium are two exciting cases. They are the only known solids that become disordered when cooled. Their low-temperature structures have been debated for decades with many conflicting experimental findings. I will propose an explanation that borrows ideas from the field of frustrated magnetism. At low temperatures, lithium and sodium form close-packed structures with stacked triangular layers. Due to a hidden gauge symmetry, all stacking configurations are nearly degenerate. An infinite family of crystal structures compete with one another, giving rise to a seemingly random structure. This 'frustration' is a quantum effect, analogous to the Aharonov-Bohm phase that emerges in a particle moving on a ring. Reference: arXiv:2405.15865