High-order Van Hove singularities and their connection to flat bands

Abstract

The flattening of single-particle band structures plays an important role in the quest for novel quantum states of matter due to the crucial role of interactions. Recent advances in theory and experiment made it possible to construct and tune systems with nearly flat bands, ranging from graphene multilayers and moire' materials to kagome' metals and ruthenates. While theoretical models predict exactly flat bands under certain ideal conditions, evidence was provided that these systems host high-order Van Hove points, i.e., points of high local band flatness and power-law divergence in energy of the density of states. In this review, we examine recent developments in engineering and realising such weakly dispersive bands. We focus on high-order Van Hove singularities and explore their connection to exactly flat bands. We provide classification schemes and discuss interaction effects. We also review experimental evidence for high-order Van Hove singularities and point out future research directions.

Review article, to appear in Annual Review of Condensed Matter Physics

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Cited by in corpus (12)

• On the engineering of higher-order Van Hove singularities in two dimensions
• Spin and pair density waves in 2D altermagnetic metals
• Superconductivity and pair density waves from nearest-neighbor interactions in frustrated lattice geometries
• Designing Topological High-Order Van Hove Singularities: Twisted Bilayer Kagomé
• Mean-field analysis of a Hubbard interaction on Bernal Bilayer Graphene
• Van-Hove singularities and competing instabilities in an altermagnetic metal
• Brightening dark excitons and trions in systems with a Mexican-hat energy dispersion: example of InSe
• Kekulé order from diffuse nesting near higher-order Van Hove points
• Anisotropic scattering rates in strain-tuned Sr${}_2$RuO${}_4$
• Triplet superconductivity supported by an X${}_9$ high-order Van Hove singularity
• Strain Engineering of van Hove Singularity and Coupled Itinerant Ferromagnetism in Quasi-2D Oxide Superlattices
• Weak localization and universal conductance fluctuations in large area twisted bilayer graphene