[Paper Review] Observation of Quadratic (Charge-2) Weyl Point Splitting in Near-Infrared Photonic Crystals

Christina Jörg, Sachin Vaidya+5 more|arXiv (Cornell University)|Jun 22, 2021

Topological Materials and Phenomena42 references27 citations

TL;DR

This paper experimentally demonstrates the splitting of a quadratic (charge-2) Weyl point into two linear (charge-1) Weyl points in a micro-3D printed near-infrared photonic crystal. By breaking screw symmetry via controlled geometric defects in a chiral woodpile structure, the authors observe topologically protected Weyl point splitting along high-symmetry directions in momentum space, confirmed by Fourier-transform infrared spectroscopy and symmetry-based theoretical analysis.

ABSTRACT

Weyl points are point degeneracies that occur in momentum space of periodic materials, and are associated with a quantized topological charge. We experimentally observe in a 3D micro-printed photonic crystal that a charge-2 Weyl point can be split into two charge-1 Weyl points as the protecting symmetry of the original charge-2 Weyl point is broken. Moreover, we use a theoretical analysis to confirm where the charge-1 Weyl points move within the Brillouin zone as the strength of the symmetry breaking increases, and confirm it in experiments using Fourier-transform infrared spectrometry. This micro-scale observation and control of Weyl points is important for realizing robust topological devices in the near-infrared.

Motivation & Objective

• To experimentally observe the splitting of a quadratic (charge-2) Weyl point into two linear (charge-1) Weyl points in a 3D photonic crystal.
• To investigate the role of symmetry breaking—specifically, the reduction of screw symmetry—in enabling controlled Weyl point splitting.
• To demonstrate momentum-space control of Weyl point separation through geometric tuning of the photonic crystal structure.
• To validate the topological nature of the Weyl points using Berry phase measurements and symmetry analysis.
• To establish a micron-scale, near-infrared platform for topological photonics with tunable Weyl points for device applications.

Proposed method

• Fabrication of a chiral woodpile photonic crystal using two-photon polymerization with a lattice constant of 2.1 µm and dielectric constant ε = 2.31.
• Introduction of a width defect (w0 ≠ w) in one layer of the unit cell to break the P4222 space group and reduce symmetry to P222.
• Use of Fourier-transform infrared (FTIR) spectroscopy to measure angle-resolved transmission spectra and identify Weyl point positions.
• Theoretical modeling using group theory and symmetry analysis to predict splitting directions along high-symmetry lines in the Brillouin zone.
• Numerical simulations via RCWA and MPB to compute bulk bands and compare with experimental data.
• Berry phase analysis of band structures to confirm topological charge: double winding for quadratic WP (charge-2), single winding for linear WPs (charge-1).

Experimental results

Research questions

• RQ1 Can a quadratic (charge-2) Weyl point be experimentally split into two linear (charge-1) Weyl points in a 3D photonic crystal?
• RQ2 What symmetry constraints govern the momentum-space splitting direction of Weyl points upon symmetry breaking?
• RQ3 How does geometric tuning of the photonic crystal structure control the separation of the resulting linear Weyl points?
• RQ4 Can the topological nature of the Weyl points be confirmed experimentally via Berry phase measurements?
• RQ5 Is it feasible to realize tunable, topologically protected Weyl points in micron-scale, near-infrared photonic crystals?

Key findings

• The quadratic Weyl point at the Γ point in the original chiral woodpile structure (P4222 space group) splits into two linear Weyl points upon introduction of a width defect in one layer.
• The splitting occurs exclusively along high-symmetry directions in momentum space (e.g., Γ–Y), as predicted by symmetry analysis of the reduced P222 space group.
• Experimental FTIR spectra show clear signatures of Weyl point formation: sharp transmission dips at the Weyl point frequencies, with momentum-space separation tunable via geometric parameters.
• Berry phase measurements confirm the topological charge: double winding (charge-2) at the original Γ point and single winding (charge-1) at each of the two split points.
• The momentum-space separation between the two linear Weyl points increases with increasing width mismatch (w0 − w), demonstrating geometric control.
• The observed Weyl point splitting is robust and reproducible across multiple fabricated samples, confirming the role of symmetry breaking in enabling topological control.