Abstract: Close-packing of spheres is a problem with a long, beautiful history that spans centuries. To achieve maximal density, we must first arrange spheres into triangular layers and stack them. Each layer can sit in two possible positions. I will describe the solid that arises from random stacking, i.e., when each twofold choice is made at random. I will introduce a related problem — that of stacking spheres with the least possible density, while retaining stability. The conjectured solution involves stacking honeycomb layers, with a six-fold choice at each layer.  I will describe random stacking in this case as well.

I will then present a decades-long puzzle: the low-temperature structure of lithium and sodium. Both have irregular structures with many conflicting claims. We propose an explanation that borrows ideas from the field of frustrated magnetism. Lithium and sodium form close-packed structures, with stacked triangular layers. Due to a hidden gauge symmetry, all stacking configurations have the same electronic energy. We have a ‘frustrated’ solid where an infinite family of crystal structures compete.

References: Phys. Rev. E 108, 035003 (2023),arXiv:2405.15865

Speaker Bio: Ganesh Ramachandran obtained his PhD from the University of Toronto in 2011. He then completed a postdoctoral stint at IFW, Dresden. Subsequently, he was a faculty member at the Institute of Mathematical Sciences in Chennai, India. Since 2021, he has been an Assistant Professor at Brock University.

Prof. Ramachandran has worked on frustrated magnetism, topological phases, quantum state preparation and statistical physics. His recent work touches upon pump-induced correlations, altermagnetism, spin ice and quantum dimer models.