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Abstract Graphene, with its two linearly dispersing Dirac points with opposite windings, is the minimal topological nodal configuration in the hexagonal Brillouin zone. Topological semimetals with higher-order nodes beyond the Dirac points have recently attracted considerable interest due to their rich chiral physics and their potential for the design of next-generation integrated devices. Here we report the experimental realization of the topological semimetal with quadratic nodes in a photonic microring lattice. Our structure hosts a robust second-order node at the center of the Brillouin zone and two Dirac points at the Brillouin zone boundary—the second minimal configuration, next to graphene, that satisfies the Nielsen–Ninomiya theorem. The symmetry-protected quadratic nodal point, together with the Dirac points, leads to the coexistence of massive and massless components in a hybrid chiral particle. This gives rise to unique transport properties, which we demonstrate by directly imaging simultaneous Klein and anti-Klein tunnelling in the microring lattice.
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This content will become publicly available on March 17, 2026
Semi-classical limit of the Dirac equation in curved space and applications to strained and photonic graphene
Abstract The semi-classical regime of static Dirac matter is derived from the Dirac equation in curved space-time. The leading- and next-to-leading-order contributions to the semi-classical approximation are evaluated. While the leading-order yields classical equations of motion with relativistic Lorentz and a geometric forces related to space curvature, the next-to-leading-order gives a transport-like equation with source terms. We apply the proposed strategy to the simulation of electron propagation on strained graphene surfaces, as well as to the dynamics of edge states in photonic graphene.
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- Award ID(s):
- 2109116
- PAR ID:
- 10633908
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Journal of Physics A: Mathematical and Theoretical
- Volume:
- 58
- Issue:
- 11
- ISSN:
- 1751-8113
- Page Range / eLocation ID:
- 115302
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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