Interplay between electronic nematicity and acoustic phonons in cubic lattices

Electronic nematicity, a state that spontaneously breaks rotational symmetry, has been widely investigated in tetragonal and hexagonal systems, where it is described by an Ising or a 3-state Potts order parameter, respectively. The nematic critical properties in these lattices are known to be strongly impacted by the underlying crystalline medium via the nemato-elastic coupling, since acoustic phonons mediate anisotropic long range nematic interactions. In this work, we investigate the intrinsically coupled nematic and elastic phenomena on the relatively unexplored cubic lattice. We find that two types of nematic order emerge: 3-state Potts (Z₃) nematicity, associated with the breaking of threefold rotational symmetry, and 4-state Potts (Z₄) nematicity, related to fourfold rotations. We calculate the contribution of the acoustic phonons to the nematic self-energy and find that, although in both cases the nematic mass softens only along certain momentum-space directions, in the Z₄ case the nematic director is significantly rotated by the phonon-mediated interactions whereas in the Z₃ case the nematic director is unaffected by them.