Since the 1970s, scientists have observed that certain organic polymers—long chains of carbon molecules—can interact with light in unusual ways. Specifically, these materials can mix three photons together, creating strong electrical response in the material called hyperpolarizability, which arise from electrons being “pushed around” by light in special ways.

However, a long-standing puzzle remained: some polymers with the exact same chemical bonds, but with atoms arranged differently, show drastically different responses to light. Until now, researchers overlooked a key factor: the shape and connectivity of the electrons’ quantum states, also known as their topology and geometry.

In a new study published in Physical Review Letters, Dr. Michele Pizzochero from the Department of Physics at the University of Bath, together with collaborators from the Universities of Cambridge and Manchester, has demonstrated that the intricate mathematical properties of electrons—shaped by the way their wavefunctions twist and interconnect—play a significant role in determining their optical behaviour. By examining polymers like cis- and trans-polyacetylene, we recognised that their electrons’ wavefunctions have different topologies. This explains why these systems respond so differently to light: the “shape” of their quantum states affects how easily they can be polarised.

Importantly, these findings offer a design principles to control these effects. By stretching the material or applying other external stimuli, we predict that the geometry of the electron wavefunctions can tune the optical response of materials. These advances may open the door to new types of optical and electronic devices, based on a deeper understanding of the hidden twists in electrons' quantum behaviour.

Reference:
W. Jankowski, R- J. Slager, M. Pizzochero
Enhancing the hyperpolarizability of crystals with quantum geometry
Physical Review Letters 135, 126606 (2025)