Quantum geometry, topology, and materials

Orbital interference and frustrated hopping in the two-dimensional metal Pd₅AlI₂. Figure from Nature Physics 21, 1260–1266 (2025).

Geometry as the language of bonding and response

Bloch bands describe extended waves, yet electrons in solids also form local bonds and orbitals. Quantum geometry connects these pictures. The quantum metric and Berry curvature quantify how wavefunctions change across momentum space, setting otherwise hidden scales for polarization, capacitance, optical response, collective modes, and transport.

We combine general theory with material-specific modeling and experiment. Work on Pd₅AlI₂ and real-space topology is carried out with experimental collaborators including Xavier Roy’s group and Abhay Pasupathy’s group, linking orbital structure directly to spectroscopy and scanning-probe measurements.

Selected papers

• Quantum Geometry and the Hidden Scales in Materials — Nature Reviews Physics 8, 226–239 (2026).
• Real-Space Imaging of the Band Topology of Transition Metal Dichalcogenides — Nature Physics 22, 680–685 (2026).
• Frustrated electron hopping from the orbital configuration in a two-dimensional lattice — Nature Physics 21, 1260–1266 (2025).
• Instantaneous Response and Quantum Geometry of Insulators — PNAS 122, e2405837122 (2025).
• Framework to Measure Quantum Metric from Step Response — Physical Review Letters 134, 106403 (2025).
• The quantum geometric origin of capacitance in insulators — Nature Communications 15, 4621 (2024).
• Semi-Dirac Fermions in a Topological Metal — Physical Review X 14, 041057 (2024).