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

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 $V_{\mathrm{el}}(q)=q\mathcal{G}(q)$ with $\mathcal{G}(0)\propto (m_h-m_e)/(m_h+m_e)$, vanishing identically for equal masses (parity protection). A multipole interference factor ${\mathcal{I}}_n={\beta }_e^n-(-{\beta }_h{)}^n$ 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.

arXiv comment7 pages, 5 figures, 1 table