Geometric Quantum Matter

• Applicant: Dr. Johannes Mitscherling
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 568440758

Quantum geometry allows a precise description of coherent superpositions formed by Bloch electrons in crystals and helps to better understand phenomena in novel classes of materials such as Kagome metals, Moiré heterostructures, and altermagnets. The superposition of atomic orbitals, spin, and other degrees of freedom is characterized by topological and geometric invariants that explain, for example, quantized and non-linear transport properties. Furthermore, the quantum geometry of Bloch electrons is essential for understanding exotic many-body phenomena, as recently demonstrated for the fractional quantum Hall effect at zero magnetic fields in twisted transition metal dichalcogenides. The quantum metric and the Berry curvature are geometric invariants that describe many phenomena, but in particular, non-linear optics and the physics of interacting flatband systems require further geometric invariants. Based on first promising results, this project will lay the foundation for a comprehensive geometric classification of quantum materials, phenomena, and experimental techniques. A deep understanding of the quantum geometry of materials within a unified theory will allow the identification of common quantum geometric origins of phenomena and the comparison and tailoring of materials via their quantum geometric properties. This project consists of three lines of research. In the first research line, we will search for non-linear response functions in unconventional magnets and excitonic matter based on novel quantum geometric invariants such as torsion and non-Abelian quantum geometry. Many standard methods do not apply to flatband systems due to the constant energy-momentum relation and, thus, require new theoretical concepts. Therefore, we will develop a microscopic theory of electron transport in interacting flatband systems in the second research line. It is already known that novel global geometric invariants are needed. Using this theory, we will investigate what we can learn from the transport properties at higher temperatures about the emergent exotic phases at lower temperatures. In the third research line, we will use lattice deformations and magnetic structures to tailor quantum geometric and correlated phenomena. In conclusion, this project represents a significant step towards a comprehensive description of the physics arising in novel material classes beyond their spectral and topological properties, and towards a better understanding of the emergent many-body phenomena in geometric quantum matter.

• DFG Programme: Emmy Noether Independent Junior Research Groups