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Annual Review of Condensed Matter Physics

Volume 16, 2025

High-Order Van Hove Singularities and Their Connection to Flat Bands

  • Laura Classen1,2 and Joseph J. Betouras3
  • 1Max Planck Institute for Solid State Research, Stuttgart, Germany 2Department of Physics, Technical University of Munich, Garching, Germany 3Department of Physics and Centre for the Science of Materials, Loughborough University, Loughborough, United Kingdom; email: [email protected]
  • Vol. 16:229-251 (Volume publication date March 2025)
  • First published as a Review in Advance on November 15, 2024
  • Copyright © 2025 by the author(s).
    This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. See credit lines of images or other third-party material in this article for license information.

Abstract

The flattening of single-particle band structures plays an important role in the quest for novel quantum states of matter owing 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 moiré materials to kagome metals and ruthenates. Although 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 realizing 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.

Keyword(s): density of states, flat bands, graphene systems, high-order Van Hove singularities, interacting systems, kagome metals, moiré materials, strontium ruthenates
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2025-03-10
2025-06-24
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/content/journals/10.1146/annurev-conmatphys-042924-015000
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High-Order Van Hove Singularities and Their Connection to Flat Bands
Annual Review of Condensed Matter Physics 16, 229 (2025); https://doi.org/10.1146/annurev-conmatphys-042924-015000
/content/journals/10.1146/annurev-conmatphys-042924-015000
/content/journals/10.1146/annurev-conmatphys-042924-015000
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