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
Electronic bound states in the continuum now in Science
Our work on electronic bound states in the continuum in Pd₅AlI₂ is now published in Science. Destructive quantum interference traps electron waves around atomic defects—even inside a metal.
Columbia Quantum features electronic bound states in the continuum
Ellen Neff’s Columbia Quantum Initiative feature, “Quantum Interference Is Key to Catching Electron Waves,” tells the story behind our Science paper on electronic bound states in the continuum in Pd₅AlI₂. Read the feature for the experiments, the quantum-interference mechanism, and the people behind the work.
New preprint: Ring states and the vacancy-driven topological transition
Peter’s new preprint with Raquel, Vacancy-driven topological transition of a Chern insulator, is on arXiv. Ring states bound to individual vacancies overlap and hybridize into an impurity band, providing a microscopic picture of how strong disorder destroys a Chern phase. Figure 1 illustrates the ring-state percolation picture.
Research Projects
Disorder and defects in topological systems
A missing atom or a disordered bond can trap an electronic state, connect conducting paths, or change how a crystal responds to an electric field. We study which of these effects are enforced by topology, and how local wavefunctions reveal them when translation symmetry is lost.
Moiré materials and correlations
Rotating one atomic layer relative to another creates a long-period pattern that can slow electrons until their interactions dominate. We study how the resulting wavefunctions select fractional phases, magnetism, and collective order. Local-orbital models and continuum theory connect that microscopic structure to optical and transport measurements.
Symmetry and topological characterization of quantum materials
An electron in a crystal spreads over atoms and bonds, and its wavefunction changes as it moves through the band. We connect this spatial structure to band topology and quantum geometry, then identify its signatures in tunnelling images, optical spectra, and electrical response. Our material models keep the orbital structure that makes those signatures possible.
Transport and collective behavior of quantum devices
An electric field moves charge between atoms, across a sample, and through collective modes. We connect these motions to the geometry of electronic wavefunctions and identify measurements that distinguish them. Optical spectral weight, capacitance, kinetic inductance, and local Hall fields let us test microscopic theory in working devices.
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