Topology, geometry, and quantum matter
We study how symmetry, topology, and quantum geometry shape electronic structure and collective behavior—from real-space defects and moiré flat bands to measurable response in quantum materials.
News
Geometric response of metals across long and short times
Nish’s manuscript develops a geometric description of metallic response across long and short times and is now on arXiv.
Columbia MRSEC renewed through 2032
The NSF has renewed Columbia’s Materials Research Science and Engineering Center for six years. Our group is part of IRG2 on nonequilibrium quantum metamaterials, developing theory for driven topological phases and quantum geometry in materials coupled to cavities.
ARO Early Career Program award
The Army Research Office has funded our project, “Quantum Geometry as a Knob of Collective Phenomena in 2D Superlattices.” The project will develop moiré models that retain spatial orbital embedding and use them to predict geometric signatures in collective modes and superconductivity.
Research Projects
Disorder, defects, and real-space topology
Topological phases are most revealing where translation symmetry breaks: at defects, boundaries, and through disorder. We study the real-space states and dynamical responses that survive imperfect crystals, and how local modes reorganize transport and screening.
Moiré, correlations, and collective phenomena
In moiré materials, geometry and interactions become tunable on the same energy scale. We study how flat topological bands generate fractional phases, magnetism, superconductivity, and collective modes—and how those states appear in transport, optics, and time-resolved probes.
Quantum geometry, topology, and materials
Quantum geometry measures how electrons are localized and bonded inside a crystal; topology records the obstructions to that localization. We connect both to measurable energy scales and responses in real materials—from capacitance and optics to scanning probes and transport, with Pd5AlI2 as a central material platform.