Phase competition in quantum materials with higher order van Hove singularities

Although the route towards many phases in quantum materials is an open question that admits several answers, for the formation of Density Waves a good candidate is believed to be Fermi surfaces nesting in various materials e.g iron pnictides, organics and transition metals. The motivation of this work came from the physics of Sr₃Ru₂O₇, but the model we treat is very general. First we review recent works aiming to understand whether nesting itself is capable to generate SDW order and we show that indeed Density Waves can be formed between two nearly nested Fermi Surfaces. We present a very general scenario in order to study the fate of the SDW phase primarily formed between the nearly nested patches in the case when a higher order Van Hove singularity emerges as the chemical potential is tuned. We study the competition of the phases (SDW, CDW, superconductivity) in weak-coupling case applying the parquet RG approach. The results of this work are applicable to numerous 2D strongly correlated systems which undergo topological quantum phase transitions such as Sr₃Ru₂O₇, transition metal dichalcogenides, bilayer and twisted bilayer graphene.