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
Cell natural orbitals provide a local basis for interacting topological bands
Nish, Harshitra, and Daniel introduce Cell Natural Orbitals, a local basis that organizes interactions in topological bands through the geometry of their wavefunctions. The construction exposes a hierarchy of interaction channels and connects band topology to real-space correlations.
Cell Natural Orbitals in Quantum Materials
Harshitra, Nish, and Daniel develop Cell Natural Orbitals into a systematic local basis for quantum-material bands. Applied to twisted bilayer WSe₂, the construction identifies the orbitals needed to reproduce symmetry, charge density, and quantum geometry across twist angle.
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.
Research Projects
Disorder and defects in topological systems
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 materials and correlations
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.
Symmetry and topological characterization of quantum 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.
Transport and collective behavior of quantum devices
How do geometry and topology become measurable? We study the electrical, optical, and collective response of quantum materials—from instantaneous geometric currents and nonlinear metal response to plasmons, kinetic inductance, and unconventional superconductivity.
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