Event Details

Crystallization is one of the most familiar but least understood phase transitions. Why some crystal structures are more common than others? What selects between different close-packed orderings? Why do atoms sometimes prefer to arrange themselves into quasi-crystals, which correspond to projections from 5 or 6 dimensional lattices? I will show that in metallic alloys, the energetics is strongly influenced by sharp electronic Fermi surface, which favors rhombohedral, FCC, and icosahedral quasicrystal lattices for simple geometric reasons.

In the second — “time” — part of the talk, I will apply the cut-projection ideas from quasicrystals to driven systems, allowing creating multiple time dimensions, and topological band structures even starting from zero-dimensional physical systems.

Refs:
Ivar Martin, Sarang Gopalakrishnan, Eugene Demler, “Weak crystallization theory of metallic alloys”, Phys. Rev. B 93, 235140.
Ivar Martin, Gil Refael, and Bertrand Halperin, “Topological frequency conversion in strongly driven quantum systems,” arXiv:1612.02143