Topology Obstructs Nodeless Excitons

@misc{eek2026topology,
  title = {{Topology Obstructs Nodeless Excitons}},
  author = {Lumen Eek},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36248},
  eprint = {2609.36248},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36248},
}

TY  - UNPB
TI  - Topology Obstructs Nodeless Excitons
AU  - Lumen Eek
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.36248
UR  - https://arxiv.org/abs/2609.36248
AB  - Lowest-energy excitons are usually expected to have nodeless 1s-like envelope wavefunctions. We show that band topology can obstruct this expectation. The exciton envelope wavefunction is a section of the valence-conduction transition bundle, whose topology can enforce momentum-space zeros, with their parity or signed total index fixed by the corresponding characteristic class. We exemplify this behavior in a minimal PT-symmetric three-band model with a rank-two transition bundle characterized by Euler number ν^e=2. By directly solving the Bethe-Salpeter equation with both contact and Rytova-Keldysh interactions, we find that the lowest exciton contains two zeros, each with index +1, and is less strongly bound than its topologically trivial counterpart. We further classify topology-enforced exciton nodal structures for real and complex transition bundles in dimensions d ≤ 3. Our results establish the topology of the transition bundle as a direct constraint on exciton wavefunctions and spectra.
ER  -