Symmetry-protected intraband exciton-phonon scattering and its breakdown by mass asymmetry
Abstract
The coupling of excitons to lattice vibrations is typically treated via phenomenological models that artificially separate long-range Fröhlich and short-range Holstein interactions. Recent analytical work has established that, in the delocalized limit, Fröhlich scattering is suppressed by electron--hole interference. Here we present a model-space Bethe--Salpeter framework to evaluate exciton--phonon coupling across the extended-to-localized crossover. We establish a fundamental distinction between the \emph{inclusive} exciton--phonon coupling weight, obtainable via an exact completeness sum rule without summation over excited states, and the \emph{exclusive} intraband (internal-state-preserving) scattering amplitude that governs low-energy decoherence. We prove an exact symmetry theorem: for an inversion-symmetric relative-coordinate Hamiltonian with equal electron and hole masses, the intraband Fröhlich vertex vanishes identically, protecting the exciton from low-energy polar phonon scattering. When mass asymmetry is introduced, the finite-momentum relative wavefunction acquires a complex phase twist that breaks this protection. By analyzing the long-wavelength limit, we derive a controlled small-q activation law showing that the intraband vertex scales as F00(q) ∝ Δq2 ⟨ r2 ⟩, where Δ parameterizes the mass asymmetry. Finally, we compute the second-order polaron self-energy shift and demonstrate that mass asymmetry dramatically enhances phonon dressing, confirming that the symmetry theorem directly governs the many-body energy renormalization of the exciton. These results provide a rigorous conceptual framework for understanding the competition between long-range and local exciton--phonon coupling in polar semiconductors.
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BibTeX
@misc{atambo2026symmetryprotected,
title = {{Symmetry-protected intraband exciton-phonon scattering and its breakdown by mass asymmetry}},
author = {Michael O. Atambo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29634},
eprint = {2609.29634},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29634},
}
RIS
TY - UNPB
TI - Symmetry-protected intraband exciton-phonon scattering and its breakdown by mass asymmetry
AU - Michael O. Atambo
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29634
UR - https://arxiv.org/abs/2609.29634
AB - The coupling of excitons to lattice vibrations is typically treated via phenomenological models that artificially separate long-range Fröhlich and short-range Holstein interactions. Recent analytical work has established that, in the delocalized limit, Fröhlich scattering is suppressed by electron--hole interference. Here we present a model-space Bethe--Salpeter framework to evaluate exciton--phonon coupling across the extended-to-localized crossover. We establish a fundamental distinction between the \emph{inclusive} exciton--phonon coupling weight, obtainable via an exact completeness sum rule without summation over excited states, and the \emph{exclusive} intraband (internal-state-preserving) scattering amplitude that governs low-energy decoherence. We prove an exact symmetry theorem: for an inversion-symmetric relative-coordinate Hamiltonian with equal electron and hole masses, the intraband Fröhlich vertex vanishes identically, protecting the exciton from low-energy polar phonon scattering. When mass asymmetry is introduced, the finite-momentum relative wavefunction acquires a complex phase twist that breaks this protection. By analyzing the long-wavelength limit, we derive a controlled small-q activation law showing that the intraband vertex scales as F_00(q) ∝ Δq^2 ⟨ r^2 ⟩, where Δ parameterizes the mass asymmetry. Finally, we compute the second-order polaron self-energy shift and demonstrate that mass asymmetry dramatically enhances phonon dressing, confirming that the symmetry theorem directly governs the many-body energy renormalization of the exciton. These results provide a rigorous conceptual framework for understanding the competition between long-range and local exciton--phonon coupling in polar semiconductors.
ER -