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One-Dimensional Frenkel and Wannier Excitons in Electric Fields: Stark Effect, Ionization, Polarizability and Electroabsorption

One-dimensional semiconductors are characterized by strongly bound excitons. Therefore, the Frenkel regime of excitons localized within a few unit cells is readily reached and traditional Wannier exciton models become inadequate. In the presence of strong electric fields, excitons are polarized and, in extreme cases, ionized. Such strong-field effects have previously been described analytically for Wannier excitons. In the present work, we show that analytical results can be extended to the more involved Frenkel case as well. Hence, by analytically solving the difference equation describing Frenkel excitons in electric fields, we derive close-form expressions for resonances providing Stark shifts and ionization rates. Moreover, closed-form results for exciton electroabsorption spectra and dynamic polarizability are obtained.