Revealing Tensor Monopoles through Quantum-Metric Measurements

Area of Science:

• Condensed matter physics
• High-energy physics
• Topological states of matter

Background:

• Monopoles are key topological objects in gauge theories and topological states.
• Conventional monopoles exist in odd dimensions (e.g., Dirac monopole in 3D, Yang monopole in 5D).
• Exotic tensor monopoles, linked to tensor gauge fields, are predicted in even dimensions, specifically 4D.

Purpose of the Study:

• Investigate the creation and measurement of tensor monopoles in condensed matter.
• Introduce a realistic three-band model in a four-dimensional parameter space for tensor monopole studies.
• Relate tensor monopole topological charge to generalized Berry curvature and quantum metric.

Main Methods:

• Developed a realistic three-band model in a 4D parameter space.
• Proposed a probing method based on extracting topological charge from the quantum metric.
• Linked the topological charge to a generalized Berry curvature.

Main Results:

• Demonstrated the theoretical possibility of creating tensor monopoles in a condensed-matter system.
• Established a connection between tensor monopoles and the quantum metric.
• Proposed a method for experimental detection using quantum-metric measurements.

Conclusions:

• Tensor monopoles can potentially be realized and measured in condensed-matter systems.
• Quantum metric measurements offer a viable pathway to probe these exotic topological objects.
• A realistic three-level atomic system is proposed for generating and observing tensor monopoles.