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  • Open Access

Enhancing the Hyperpolarizability of Crystals with Quantum Geometry

Wojciech J. Jankowski1,*, Robert-Jan Slager2,1, and Michele Pizzochero3,4,†

  • *Contact author: wjj25@cam.ac.uk
  • †Contact author: mp2834@bath.ac.uk
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Phys. Rev. Lett. 135, 126606 – Published 16 September, 2025

DOI: https://doi.org/10.1103/z7lp-pqp6

Abstract

We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional π-conjugated chains as representative model systems. First, we show that the crystalline-symmetry-protected topology of these chains imposes a lower bound on their quantum metric and hyperpolarizabilities. Second, we employ numerical simulations to reveal the tunability of nonlinear, quantum geometry-driven optical responses in various one-dimensional crystals in which band topology can be externally controlled. Third, we develop a semiclassical picture to deliver an intuitive understanding of these effects. Our findings offer a firm interpretation of otherwise elusive experimental observations of colossal hyperpolarizabilities and establish guidelines for designing topological materials of any dimensionality with enhanced nonlinear optical properties.

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Phys. Rev. Lett. 135, 126606– Published 16 September, 2025
  • Received 10 February 2025
  • Revised 26 June 2025
  • Accepted 19 August 2025
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