Classification of electronic nematicity in three-dimensional crystals and quasicrystals

Electronic nematicity, proposed as a novel correlated state of matter more than two decades ago, is being reported in an ever-growing number of materials. Yet, research on this topic has focused on realizations in quasi-two-dimensional lattices with fourfold or sixfold rotational symmetries. This work presents a systematic and unifying classification scheme for electronic nematicity in all crystallographic point groups and noncrystallographic groups relevant to quasicrystals and twisted materials. It reveals a rich nematic phenomenology described in terms of distinct types of Potts and clock models.