Enhancing the Hyperpolarizability of Crystals with Quantum Geometry

TL;DR

This paper shows how quantum geometry and topological invariants can be used to enhance and understand the nonlinear optical properties of crystals, especially hyperpolarizability, through theoretical and numerical methods.

Contribution

It introduces a topological and quantum geometric framework for enhancing hyperpolarizability in crystals, providing new design principles for nonlinear optical materials.

Findings

Topological invariants impose bounds on hyperpolarizability.

Band topology can be externally tuned to control optical responses.

A semiclassical model explains the quantum geometry effects.

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 $\pi$-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.