Matrix Density Waves and Fractionally Charged Point Defects in Flavor Weyl Semimetals
Abstract
A conventional interaction-driven Weyl density wave is a complex scalar and supports vortex lines, but no topologically stable point defects. We show that two Weyl flavors do not merely duplicate this order. Starting from the matrix-valued internode coherence, a local flavor-symmetric repulsion selects a traceless adjoint condensate within the density-wave sector, while the fermionic ground-state energy locks its complex components into the collinear form Δ=Φ0n eiθ. The resulting order-parameter manifold, (S2× S1)/ℤ2, supports both unit hedgehogs and half-quantum Alice strings of the same electronic mass that gaps the Weyl fermions. An elementary hedgehog binds a single normalizable zero mode whose empty and occupied sectors carry charges −e/2 and +e/2 at neutrality. An elementary Alice string carries a single chiral electronic mode despite its π phase winding, and transporting a hedgehog around it reverses the hedgehog winding, N→−N. Flavor therefore converts spontaneous translation breaking into a route to point-defect fractionalization and intertwines the point- and line-defect sectors of an interaction-generated electronic mass.
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BibTeX
@misc{mukherjee2026matrix,
title = {{Matrix Density Waves and Fractionally Charged Point Defects in Flavor Weyl Semimetals}},
author = {Shantonu Mukherjee and Hridis K. Pal},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26957},
eprint = {2609.26957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26957},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Matrix Density Waves and Fractionally Charged Point Defects in Flavor Weyl Semimetals
AU - Shantonu Mukherjee
AU - Hridis K. Pal
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.26957
UR - https://arxiv.org/abs/2609.26957
AB - A conventional interaction-driven Weyl density wave is a complex scalar and supports vortex lines, but no topologically stable point defects. We show that two Weyl flavors do not merely duplicate this order. Starting from the matrix-valued internode coherence, a local flavor-symmetric repulsion selects a traceless adjoint condensate within the density-wave sector, while the fermionic ground-state energy locks its complex components into the collinear form Δ=Φ_0n e^iθ. The resulting order-parameter manifold, (S^2× S^1)/ℤ_2, supports both unit hedgehogs and half-quantum Alice strings of the same electronic mass that gaps the Weyl fermions. An elementary hedgehog binds a single normalizable zero mode whose empty and occupied sectors carry charges −e/2 and +e/2 at neutrality. An elementary Alice string carries a single chiral electronic mode despite its π phase winding, and transporting a hedgehog around it reverses the hedgehog winding, N→−N. Flavor therefore converts spontaneous translation breaking into a route to point-defect fractionalization and intertwines the point- and line-defect sectors of an interaction-generated electronic mass.
ER -