Unconventional bond- and current-density waves on hexagonal lattices

Abstract

Charge-density wave (CDW) orders are conventionally described as modulations of on-site charge at an ordering wave vector $\boldsymbol{Q}$ with symmetry-related wave vectors typically forming a multicomponent order-parameter manifold. Recent developments significantly broadened this phenomenology to bond and loop-current density waves, which possess nontrivial, potentially symmetry-breaking textures within the unit cell in addition to their spatial modulation at $\boldsymbol{Q}$. Such textures arise from particle-hole condensates with nonzero angular momentum, analogous to unconventional superconductivity, and their symmetries are described by the little group $G_{\boldsymbol{Q}}$. In this work, we develop a framework for unconventional CDW phases that simultaneously incorporates the local symmetries described by little group and the presence of multiple symmetry-related ordering wave vectors, also known as the star. The resulting multicomponent order parameter transforms under representations of the full space group induced from irreducible representations of