A sharp split in the calculation
A theoretical calculation points to a sharp split in how excitons couple to long-wavelength phonons. In the model, elastic scattering between exciton states with the same parity loses the long-range 1/q Frohlich divergence through destructive interference. Opposite-parity inelastic transitions retain finite macroscopic coupling through constructive interference. The proposed selection rule links the outcome to whether the two internal states share the same spatial symmetry. It is a result from a theoretical model, so the central finding concerns the modeled interaction rather than a direct material measurement.
The difference appears in the low-momentum limit. For same-parity elastic scattering, the form factor scales as q to the fourth power and the effective coupling scales as q to the second power. For opposite-parity inelastic scattering, the leading form-factor term scales as q to the first power and the effective coupling scales as q to the zeroth power, leaving a finite interaction as momentum becomes small. In ordinary terms, the elastic channel fades more rapidly toward the low-momentum limit, while the inelastic channel retains its long-range contribution.
Numbers behind the rule
To test those asymptotic expressions, the study uses a standard Frohlich Hamiltonian and compares a multipole expansion with exact numerical integration of excitonic form factors. Its modeled internal states are hydrogenic 1s and 2p envelope states, including 1s to 1s elastic and 1s to 2p inelastic transitions. Leading coefficients are extracted by numerical differentiation at q times aX = 0.001, and total dressing is calculated by integrating the squared matrix element over the 3D Brillouin zone.
The reported leading coefficients are 0.300000 for the 1s to 1s channel and 0.744934 for the 1s to 2p channel. Within the stated model, the numerical values agree with the analytical expansion. That agreement is an internal validation of the model's low-momentum result, not a measurement of a real material. The supplied analysis reports no statistical uncertainty or confidence interval for these outputs.
Mass imbalance weakens elastic protection
Mass asymmetry changes the balance, especially for the elastic branch. At fixed q times aX = 0.5, increasing eta from 0.00 to 0.80 raises the squared elastic form factor from 0.000000 to 0.008612. Across the same range, the squared inelastic form factor drops from 0.117702 to 0.087601. The calculation links unequal electron and hole masses with weaker elastic protection, while the inelastic channel remains the finite-coupling branch.
An integrated dressing calculation shows the effect across the modeled momentum range. The model identifies three regimes for the dressing parameter: perfect protection, partial protection, and broken protection. At dimensionless exciton size Lambda = 15.8, the elastic dressing parameter lambda_ss rises from 0.0000 at eta = 0.00 to 0.8724 at eta = 0.80. Over the same endpoints, the inelastic parameter lambda_sp changes only from 0.6435 to 0.6348. In these tabulated cases, elastic dressing varies strongly with mass asymmetry, while inelastic dressing stays nearly constant.
The pattern is extended beyond three dimensions
The authors extend the rule analytically to two-dimensional systems. The paper states that the destructive and constructive interference mechanisms are dimensionally invariant across bulk and 2D systems. In 2D, the elastic effective coupling scales as q to the second power and the inelastic effective coupling as q to the zeroth power. After integration to a momentum cutoff, elastic dressing scales as qmax to the fourth power, compared with qmax to the second power for inelastic dressing. The model therefore retains stronger integrated suppression for the elastic channel.
Interlayer excitons are a separate case in the extension. When the electron and hole couple to distinct phonon operators, the document reports that destructive cross-cancellation vanishes and both elastic and inelastic couplings are unsuppressed. In the paper's three-regime language, this is the broken-protection case, unlike the same-parity intralayer calculation.
A framework, not a material verdict
The scope of the result is set by the calculation itself. It uses a minimal hydrogenic framework with validation centered on 3D 1s and 2p envelope states, and it is built around the stated Frohlich interaction. The reported powers and dressing values should therefore be read as outputs of that framework. They do not establish that the same numbers apply unchanged to every real material, screening environment, or phonon mode.
The paper maps halide perovskites, monolayer TMDs, and rutile TiO2 to Regimes I, II, and III, respectively. In the model's vocabulary, those regimes represent perfect protection, partial protection, and broken protection. The mapping is a theoretical connection to representative materials, not a direct experimental test of their phonon response.
The document is a preprint, arXiv:2608.25482v1, dated 26 Aug 2026. It includes an ACKNOWLEDGMENTS heading, but the supplied text does not report funding details.
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
Original paper · Full text