Engineering correlated phases through manipulation of Van Hove singularities

Abstract

Controlling the ordered phases of correlated electron systems remains a central challenge in quantum materials design. Divergences in the electronic density of states, known as Van Hove singularities (VHSs), are one obvious route to such control. It is clear from recent work that the exact functional form of these divergences can profoundly affect which phases are realized; a full picture, however, remains elusive. In this work, we use both the hot-spot parquet renormalization group and the truncated-unity functional renormalization group to theoretically study the emergent correlated states of a two-dimensional square-lattice Hubbard model with VHSs at or near the Fermi level. By varying a single hopping parameter, $t_3$, we are able to change the strength of the VHS divergence in the density of states from logarithmic (for $t_3 < t_{3c}$) to power-law (for $t_3 = t_{3c}$). Further increase of $t_3$ ($t_3 > t_{3c}$) causes each original Van Hove point to split into two, both of the conventional logarithmic type. We show that which of these regimes we are in strongly influences the predicted ordered states. We also study the dependence on doping, and find that the ferromagnetic state that occurs at Van Hove filling in these models is unstable to very small shifts in the Fermi level, often giving way to distinct ordered states depending on whether the model is electron- or hole-doped. These results highlight the importance of tuning VHS properties to control ordered states in correlated materials, and offer design rules to engineer these phases in novel systems.