Abstract

Spatially modulated orders are commonly characterized by their modulation wave vectors (Q1, Q2, ...), which define an emergent superlattice and the associated breaking of translational symmetry. However, much of the richness of density wave orders is encoded in the local symmetries and degeneracies at each Qi, desrcibed by its little group (LG), which manifest as nontrivial textures on the atomic scale. In this talk, I illustrate this through two examples, focusing on the charge and superconducting sectors.

Unconventional charge-density waves (UCDWs) encompass modulated bond or loop-current orders with nontrivial, potentially symmetry-breaking local characteristics. They arise from particle-hole condensates with nonzero angular momentum, analogous to unconventional superconductivity. We consider two-dimensional hexagonal lattices with ordering wave vectors along high-symmetry lines of the Brillouin zone (BZ). The LG at each Q necessarily admits nontrivial irreducible representations, hosting such UCDWs, while the full order parameter transforms under representations of the space group induced from these LG irreps. As a microscopic example, we consider the triangular lattice, where electronic interactions generate such instabilities near Q=K/4, upon tuning away from the van Hove filling.

We then consider a superconducting pair-density wave order with Q at BZ boundary of a nonsymmorphic lattice. Nonsymmorphic symmetries can enforce exotic degeneracies, which often occur between even- and odd-parity sectors. We show that these carry over to the order parameter, enabling multicomponent orders with components of opposite parity, even in centrosymmetric systems. This is especially consequential for superconductors, as it produces inversion-odd bilinears, which in turn can induce odd-parity secondary orders such as antiferromagnetism or electric polarization, akin to the phenomenology of multiferroic materials.

[1] A.S., H. Braun, L. Classen, arXiv:2608.19185
[2] A.S., A. Ramires, Phys. Rev. B 110, L180503