What does this research mean for the field?

The D4 dihedral group and its irreducible representations govern square-lattice symmetry and underpin the formation of Fermi arcs in Weyl semimetals, establishing a link between finite-group theory and topological band structure. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Investigate the mathematical mapping between D4 dihedral group symmetries of square lattices and topological Fermi arc surface states in Weyl semimetals.

September 8, 2026Open Access

D4 Symmetry and Fermi Arcs in Weyl Semimetals — E8 Intelligence Research

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Authors

ACAndrew Stewart Caldin

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Implication

Theoretical analysis demonstrates D4 group representations govern Fermi arc connectivity in square-lattice Weyl semimetals, indicating a finite-group basis for topological band structures.

Key Points

Investigate the mathematical mapping between D4 dihedral group symmetries of square lattices and topological Fermi arc surface states in Weyl semimetals.
Evaluated the group structure, character table, and irreducible representations of the order-8 D4 dihedral group.
Modeled topological band invariants and surface state constraints using Chern number integrations and Weyl point chiralities in the NbP semimetal family.
Mapped the two-dimensional irreducible representation of D4 to orthogonal spatial lattice directions, linking the C4 rotation subgroup to 90-degree Brillouin zone symmetry.
Showed that total Chern number changes across surface cuts equal the sum of topological chiralities of enclosed Weyl points.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9fd78a58e84d0ff5b463e8 https://doi.org/10.5281/zenodo.22471033

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Implication

Theoretical analysis demonstrates D4 group representations govern Fermi arc connectivity in square-lattice Weyl semimetals, indicating a finite-group basis for topological band structures.

D4 Symmetry and Fermi Arcs in Weyl Semimetals — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

D4 Symmetry and Fermi Arcs in Weyl Semimetals — E8 Intelligence Research

Discussion

Member takes

Implication

Key Points

Cite This Study

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