Topology and geometry under the nonlinear electromagnetic spotlight

Area of Science:

• Condensed Matter Physics
• Quantum Materials Science
• Materials Chemistry

Background:

• Traditional material characterization using dispersion spectra is often insufficient for predicting ordered phases and physical responses.
• Quantum mechanical properties, specifically the geometrical and topological characteristics of wavefunctions, are crucial for classifying certain materials.
• A significant experimental challenge lies in developing methods to probe and manipulate these quantum properties.

Purpose of the Study:

• To review recent advancements in experimental techniques for probing and controlling quantum properties in materials.
• To focus on nonlinear electromagnetic responses as a direct probe of quantum geometry and topology.
• To provide an overview of theoretical concepts, experimental approaches, and relevant materials.

Main Methods:

• Exploration of nonlinear electromagnetic responses stemming from quantum geometry and topology.
• Discussion of theoretical frameworks underpinning these phenomena.
• Analysis of experimental methodologies used to observe and control quantum topological properties.
• Examination of material systems exhibiting these properties.

Main Results:

• Recent progress in utilizing nonlinear electromagnetic responses to access quantum geometric and topological information.
• Identification of specific experimental techniques capable of probing these quantum characteristics.
• Overview of theoretical models and material candidates relevant to quantum topology.

Conclusions:

• Nonlinear electromagnetic responses offer a powerful pathway to investigate quantum geometry and topology in materials.
• Experimental techniques are advancing to probe and control emergent quantum phases.
• Integration with device architectures holds promise for uncovering and manipulating topological and correlated quantum properties.