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.
Local orbitals for quantum-material bands
Cell Natural Orbitals in Quantum Materials (arXiv, 2026).
Harshitra, Nish, and Dani construct Cell Natural Orbitals from the unit-cell one-particle density matrix to identify the local symmetric orbitals that best preserve the band geometry, charge density, and symmetry of a chosen band manifold. In twisted bilayer WSe2, the CNO spectrum tracks how orbital content changes with twist angle and provides controlled trial states for local Wannier models.
Band topology written in real-space zeros
Real-Space Imaging of Band Topology via Wavefunction Zeros (arXiv, 2026).
Julian shows that crystalline symmetry forces wavefunction zeros at specific positions inside the unit cell. Those zeros turn STM-accessible charge-density patterns into a real-space diagnostic of band topology.
Geometry as a measurable property
Our work connects Berry curvature and the quantum metric to observables in transport, spectroscopy, and real-space imaging. The aim is to turn geometric quantities into experimentally testable scales across topological and correlated materials.
Quantum Geometry and the Hidden Scales in Materials
Nature Reviews Physics 8, 226–239 (2026).
This review organizes the field around the physical scales generated by wavefunction geometry, showing how the same geometric structure controls response across insulators, metals, superconductors, and moiré systems.
Real-Space Imaging of the Band Topology of Transition Metal Dichalcogenides
Nature Physics 22, 680–685 (2026).
Atomic-scale scanning tunnelling microscopy and spectroscopy locate the valence-band Wannier center in WSe2: the K-valley density-of-states maximum lies between atomic sites, while the Γ-point maximum lies on the sites. This provides direct real-space evidence that WSe2 is an obstructed atomic insulator.
Frustrated electron hopping from the orbital configuration in a two-dimensional lattice
Nature Physics 21, 1260–1266 (2025).
In Pd5AlI2, the orbital arrangement on a primitive square lattice frustrates electron hopping and produces linear Dirac-like bands intersected at their crossing by a locally flat band. The result realizes electronic structure characteristic of Lieb and dice lattices in a non-frustrated crystal lattice.
Instantaneous Response and Quantum Geometry of Insulators
Proceedings of the National Academy of Sciences 122, e2405837122 (2025).
Extending the quantum geometric tensor to the time domain yields a gauge-invariant description of bound-electron response. The quantum metric, Chern number, optical mass, orbital magnetic moment, and dielectric permittivity emerge as successive time derivatives of the time-dependent quantum geometric tensor.
A Framework to Measure Quantum Metric from Step Response
Physical Review Letters 134, 106403 (2025).
Relaxation from constrained equilibrium implements the frequency integral in the Souza–Wilkens–Martin sum rule, providing a route to the Brillouin-zone-integrated symmetric quantum geometric tensor. The paper also notes substantial experimental challenges in extracting it from a relaxation signal.
Semi-Dirac Fermions in a Topological Metal
Physical Review X 14, 041057 (2024).
Magneto-optical spectroscopy resolves the characteristic B2/3 Landau-level scaling of semi-Dirac fermions in ZrSiS. Ab initio calculations and theoretical modeling trace the spectrum to crossing nodal lines, where quasiparticles disperse linearly in one direction and quadratically in the other.
