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  • Perspective
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Quantum geometry and the hidden scales in materials

Nature Reviews Physics volume 8, pages 226–239 (2026) Cite this article

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Abstract

Electronic properties of quantum material solids are often well understood via the low-energy dispersion of Bloch bands, motivating single-band approximations in many metals and semiconductors. However, a closer look reveals length scales and timescales introduced by quantum dipole fluctuations due to interband mixing, which are reflected in the momentum-space textures of the electronic wavefunctions. This structure is usually referred to as quantum geometry. These new scales not only qualitatively modify the linear and nonlinear responses of a material but can also have a vital role in determining the many-body ground state at low temperatures. In this Perspective, we explore how quantum geometry affects properties of materials and outline recent experimental advances that have begun to explore quantum geometric effects in various condensed matter platforms. We discuss the separation of scales that can allow us to estimate the significance of quantum geometry in various response functions.

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Fig. 1: Dipole fluctuations lead to uncertainty in electron position.
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Fig. 2: Choice of projected manifold in defining quantum metric.
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Fig. 3: Separation of scales and the emergence of a geometric length scale from lattice interference.
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Acknowledgements

R.Q. and N.V. acknowledge support from the US Department of Energy through the Center for Programmable Quantum Materials (DE-SC0019443). R.Q. also acknowledges support from the National Science Foundation CAREER program (DMR-2340394) and the Alfred P. Sloan Foundation (FG-2025-24714). P.J.W.M. acknowledges support by the European Research Council under the European Union’s Horizon research and innovation programme (XBEND, grant agreement no. 101080740). T.H. acknowledges financial support by the European Research Council (ERC) under grant QuantumCUSP (grant agreement no. 101077020).

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  1. Department of Physics, Columbia University, New York, NY, USA

    Nishchhal Verma & Raquel Queiroz

  2. Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany

    Philip J. W. Moll

  3. School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel

    Tobias Holder

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  1. Nishchhal Verma
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Verma, N., Moll, P.J.W., Holder, T. et al. Quantum geometry and the hidden scales in materials. Nat Rev Phys 8, 226–239 (2026). https://doi.org/10.1038/s42254-026-00923-y

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