Bibliographic record
Abstract
Over the last decade, Dirac matter has become one of the most prominent fields of research in contemporary material science due to the incredibly rich physics of the Dirac equation. Notable examples are the Dirac cones in graphene, Weyl points in TaAs, and gapless edge states in Bi2Te3. These unique phases of matter are intimately related to the topological structure of Dirac fermions. However, it remains an open question if the topological structure of Maxwell's equations predicts yet new phases of matter. This thesis will conclusively answer this question. Topological electrodynamics is concerned with the geometry of electromagnetic waves in condensed matter. At the microscopic level, photons couple to the dipole-carrying excitations of a material, such as plasmons and excitons, which hybridize to form new normal modes of the system. The interaction between these bosonic oscillators is the origin of temporal and spatial dispersion in optical response functions like the conductivity tensor. Our main achievement is motivating a global interpretation of these response functions, over all frequencies and wavevectors. This theory led us to the conclusion that there are topological invariants associated with the conductivity tensor itself. In this thesis, we show exactly how to calculate these electromagnetic invariants, in both continuum and lattice theories, to identify unique Maxwellian phases of matter. Magnetohydrodynamic electron fluids in strongly-correlated 2D materials like graphene are the first candidates of this new class of topological phase. The fundamental physical mechanism that gives rise to a topological electromagnetic classification is Hall viscosity which adds a nonlocal component to the Hall conductivity. To study the topological electrodynamics, we propose viscous Maxwell-Chern-Simons theory -- a Lagrangian framework that naturally generates the equations of motion, nonlocal Hall response and the boundary conditions. We demonstrate that nonlocal Hall conductivity is the spin-1 photonic equivalent of dispersive mass and induces precession of bulk photonic skyrmions. Nontrivial photonic skyrmions are associated with Dirac monopoles in the bulk momentum space and a singular Berry gauge. A singular gauge occurs when the photonic mass changes sign. Remarkably, the boundary of this medium supports gapless chiral edge states that are spin-1 helically-quantized and satisfy open boundary conditions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".