Birth Quota of Non-Generic Degeneracy Points

2022. 03. 04. 10:15
BME building F, seminar room of the Dept. of Theoretical Physics
Gergő Pintér (BME)
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[1], 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 electronic 
band structures of two- and three-dimensional crystals. 
Our work establishes a strong connection between singularity theory and 
topological band structures, and more broadly, parameter-dependent quantum systems.
[1]: Birth Quota of Non-Generic Degeneracy Points, 
Gergő Pintér, György Frank, Dániel Varjas, András Pályi, arXiv:2202.05825