2022/02/11 by Gergő Pintér, Pintér, Gergő, György Frank +5
Physics and Astronomy · #Advanced Chemical Physics Studies #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Mechanics and Non-Hermitian Physics #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2202.05825
openalex publication_date 2022/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Weyl points are generic and stable features in the energy spectrum of Hamiltonians that depend on a three-dimensional parameter space. Non-generic isolated two-fold degeneracy points, such as multi-Weyl points, split into Weyl points upon a generic perturbation that removes the fine-tuning or protecting symmetry. The number of the resulting Weyl points is at least |Q|, where Q is the topological charge associated to the non-generic degeneracy point. Here, we show that such a non-generic degeneracy point also has a birth quota, i.e., a maximum number of Weyl points that can be born from it upon any perturbation. The birth quota is a local multiplicity associated to the non-generic degeneracy point, an invariant of map germs known from singularity theory. This holds not only for the case of a three-dimensional parameter space with a Hermitian Hamiltonian, but also for the case of a two-dimensional parameter space with a chiral-symmetric Hamiltonian. We illustrate the power of this result for band structures of two- and three-dimensional crystals. Our work establishes a strong and powerful connection between singularity theory and topological band structures, and more broadly, parameter-dependent quantum systems.