Calculations in an arXiv preprint suggest that parity can decide whether a modeled exciton transition couples strongly to long-wavelength polar phonons. For same-parity elastic scattering, the analysis reports exact cancellation of the long-range infrared divergence and describes the ground-state exciton as protected at long wavelength. Opposite-parity inelastic transitions retain finite coupling.
The key comparison is between channels with matching parity labels and channels with opposite labels. The model represents the exciton with hydrogenic envelope functions, including 1s and 2p states, then examines how the electron-hole form factor changes with phonon momentum. It combines an exact multipole expansion with direct numerical integration, and the reported numerical low-momentum laws agree exactly with the expansion.
That form factor is the calculation's measure of how the modeled exciton envelope responds to a phonon. At low momentum, the same-parity elastic form factor falls as the fourth power of momentum, while its effective coupling falls as the second power. For the opposite-parity inelastic channel, the corresponding orders are second and zero, so its effective coupling remains finite as momentum approaches zero.
One fixed-momentum comparison makes the contrast concrete. With equal electron and hole masses, the squared elastic form factor was below 10⁻¹⁶, while the opposite-parity inelastic form-factor square was 0.1177. The first figure is described as machine precision, and both figures come from the model calculation.
The balance changes with mass and size
The suppression changes when the electron and hole masses become more unequal. The model tracks that imbalance with a mass-asymmetry parameter and reports progressive activation of the elastic channel through a quadrupolar term as the parameter moves from 0 to 0.8. Over the same range, the inelastic channel decreases by less than 26 percent.
Once the coupling is integrated over momentum, the analysis reports no infrared divergence in the total dressing parameter, the model's integrated measure of coupling, under its stated assumptions. In this context, an infrared divergence means a mathematical blow-up at very low momentum. The q-squared density-of-states factor cancels the inverse-q-squared Fröhlich divergence, leaving the internal form factor to govern the result up to the Brillouin-zone boundary.
Exciton size adds another axis to the picture. The conclusion describes three modeled regimes, called perfect protection, partial protection and broken protection, as size and mass asymmetry vary. In the large-size calculation at a dimensionless size of 15.8, elastic dressing rises from 0.0000 at equal masses to 0.8724 at mass asymmetry 0.80. Inelastic dressing changes only from 0.6435 to 0.6348, leaving the two modeled contributions comparable at high asymmetry.
Extensions expose the model's limits
The hierarchy remains in the paper's two-dimensional extension: elastic coupling still vanishes as momentum approaches zero, while inelastic coupling remains finite. Inelastic dressing is described as larger there by an inverse-square momentum factor. The interlayer extension changes the geometry further. With finite out-of-plane phonon momentum, a dipole term survives even for a 1s-to-1s ground-state transition, producing a zeroth-order form factor.
Those extensions also define the limits of the result. The core calculation uses hydrogenic envelopes and the long-wavelength assumptions used for the Fröhlich coupling, while the two-dimensional and interlayer cases are theoretical extensions of that framework. The reported scaling and integrated values are model-derived, with no statistical uncertainty supplied. The numerical agreement with the multipole expansion is author-reported, and the supplied analysis gives no convergence details or independent replication.
Paper data and sources
Original title: Parity-controlled electron-hole interference in exciton-phonon coupling
Authors: Michael O. Atambo
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
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