Weyl Points on Nonorientable Manifolds.

Area of Science:

• Condensed Matter Physics
• High Energy Physics
• Topological Materials

Background:

• Weyl fermions are chiral quasiparticles found in topological materials.
• The Nielsen-Ninomiya theorem restricts their chirality on orientable lattices.
• Understanding Weyl fermions on nonorientable manifolds is an open theoretical challenge.

Purpose of the Study:

• To investigate the definition and properties of Weyl points on nonorientable manifolds.
• To explore potential violations of the Nielsen-Ninomiya theorem in such systems.
• To experimentally realize and verify the predicted phenomena.

Main Methods:

• Theoretical analysis of Weyl point chirality and topology on nonorientable manifolds.
• Development of lattice models with nonsymmorphic symmetries to host these Weyl points.
• Experimental implementation and characterization in a photonic platform using synthetic momenta.

Main Results:

• Chirality of Weyl points becomes ambiguous on nonorientable manifolds, allowing non-zero total chirality.
• A new Z_{2} topological invariant associated with Weyl points on nonorientable manifolds was discovered.
• The Nielsen-Ninomiya theorem can be circumvented due to discontinuities in the Weyl point vector field.
• Experimental verification of these novel Weyl point phenomena was achieved.

Conclusions:

• The topology of quasiparticles is intrinsically linked to the topology of their underlying manifold.
• Nonorientable manifolds offer a new paradigm for realizing exotic topological phenomena, like Weyl fermions with non-zero total chirality.
• This work opens avenues for exploring novel topological physics in systems with non-trivial manifold topology.