Flat bands & topology

1. 2026 Zero-Flux Localization: Floquet Flat Bands at Magic Drives Flat Floquet bands and exact dynamical localization from a phase-space return criterion for driven quantum matter. In preparation
2. 2026 Flat-Band Bulk Photovoltaics Efficiency theory for flat-band photovoltaics, with rhombohedral pentalayer graphene as a small-gap infrared platform. In preparation
3. 2025 Zero-Flux Localization: Magic Flat Bands via Non-Abelian Gauge Fields A magnetic field that cancels out cannot trap an electron. A spin field carrying no flux of its own can — and only when the flux through one magnetic tile is a whole number of flux quanta.
4. 2025 Geometric Delocalization in Two Dimensions Two dimensions is the borderline case: a random walker in the flat plane always comes back. Crumple the plane into a surface you could actually build — flat on average, curved in patches — and the walker escapes.
5. 2025 Quantum Metamorphosis: Programmable Emergence and the Breakdown of Bulk–Edge Dichotomy in Multiscale Systems Put a whole lattice at every site of a lattice, and one dial — the ratio of the two hopping rates — carries the spectrum from one to the other. On the way across, the system is neither: bands cross and flatten, a state can be edge-like at one scale and bulk-like at the other, and the topology depends on how far away you stand.
6. 2025 A Field Theory of Localization Ph.D. Dissertation, University of Maryland, College Park ↗
7. 2024 Generic Topological Criterion for Flat Bands in Two Dimensions A flat band lets you delete time from the theory. What survives the deletion is an anomaly, and an anomaly has to come out a whole number — so the magic angle is a counting condition on the flux through one moiré cell.
8. 2024 Localizing Transitions via Interaction-Induced Flat Bands Count the zero modes of a Hamiltonian and you know whether it has a flat band. Repeat the cell and you have the band. And if a system is already close to that condition, the electrons supply the missing piece themselves — the correction costs a square and pays a straight line.

Joined on the board to Quantum anomalies, Moiré & twisted bilayers and Driven matter & light response.
Every publication, with the ones that have no page here, is on the CV.