Enhancing the Hyperpolarizability of Crystals with Quantum Geometry

Area of Science:

• Solid State Physics
• Quantum Chemistry
• Materials Science

Background:

• Higher-order electric susceptibilities, such as hyperpolarizabilities, are crucial for nonlinear optical phenomena.
• Understanding the origins of enhanced nonlinear optical responses in crystalline materials remains a key challenge.

Purpose of the Study:

• To demonstrate that topological invariants and quantum geometry enhance higher-order electric susceptibilities in crystals.
• To establish guidelines for designing topological materials with superior nonlinear optical properties.

Main Methods:

• Utilizing one-dimensional π-conjugated chains as model systems.
• Employing numerical simulations to explore tunable nonlinear optical responses.
• Developing a semiclassical picture for intuitive understanding.

Main Results:

• Crystalline-symmetry-protected topology imposes a lower bound on quantum metric and hyperpolarizabilities.
• Nonlinear optical responses are tunable and driven by quantum geometry in controlled topological crystals.
• A semiclassical model provides intuitive insight into these topological effects.

Conclusions:

• Topological invariants and quantum geometry offer a framework for understanding enhanced nonlinear optical properties.
• The findings explain previously elusive experimental observations of colossal hyperpolarizabilities.
• This work establishes principles for designing novel topological materials with tailored optical functionalities.