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Parity-selected Bethe-Salpeter equation: symmetry-adapted regularization of the exciton-phonon self-energy in polar semiconductors

  • Michael O. Atambo
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Abstract

Finite-temperature Bethe-Salpeter calculations of exciton-phonon self-energies in polar materials are bottlenecked by the Fröhlich divergence of the intra-1s scattering vertex. We show that for a bound electron-hole pair this divergence is analytically eliminated by electron-hole interference: the intra-1s vertex admits the exact factorization Vel(q)=q 𝒢(q) with 𝒢(0)∝(mh−me)/(mh+me), vanishing identically for equal masses (parity protection). A multipole interference factor ℐn=βe n−(−βh)n determines where the singularity survives-only in dipole-allowed inter-state channels. We formulate a parity-selected truncation of the exciton-phonon self-energy in which the intra-1s channel is evaluated exactly at negligible cost, converging with 102-103 fewer q-points. We find that the regularized intra-1s channel, previously obscured by numerical cutoffs, controls the temperature-dependent exciton shift in mass-asymmetric polar semiconductors.

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Cite

BibTeXRIS
BibTeX
@misc{atambo2026parityselected,
  title = {{Parity-selected Bethe-Salpeter equation: symmetry-adapted regularization of the exciton-phonon self-energy in polar semiconductors}},
  author = {Michael O. Atambo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32909},
  eprint = {2609.32909},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32909},
}
RIS
TY  - UNPB
TI  - Parity-selected Bethe-Salpeter equation: symmetry-adapted regularization of the exciton-phonon self-energy in polar semiconductors
AU  - Michael O. Atambo
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32909
UR  - https://arxiv.org/abs/2609.32909
AB  - Finite-temperature Bethe-Salpeter calculations of exciton-phonon self-energies in polar materials are bottlenecked by the Fröhlich divergence of the intra-1s scattering vertex. We show that for a bound electron-hole pair this divergence is analytically eliminated by electron-hole interference: the intra-1s vertex admits the exact factorization V_el(q)=q 𝒢(q) with 𝒢(0)∝(m_h−m_e)/(m_h+m_e), vanishing identically for equal masses (parity protection). A multipole interference factor ℐ_n=β_e^ n−(−β_h)^n determines where the singularity survives-only in dipole-allowed inter-state channels. We formulate a parity-selected truncation of the exciton-phonon self-energy in which the intra-1s channel is evaluated exactly at negligible cost, converging with 10^2-10^3 fewer q-points. We find that the regularized intra-1s channel, previously obscured by numerical cutoffs, controls the temperature-dependent exciton shift in mass-asymmetric polar semiconductors.
ER  -