Influence of dark excitons on the electroabsorption spectrum of polyacetylene

This study revisits the electroabsorption (EA) spectrum of polyacetylene, ${(\mathrm{CH})}_{\mathrm{x}}$ thin films, for both the cis- and trans-isomers, as functions of the electric field strength, isomerization degree, and light polarization states. The EA spectrum of cis-${(\mathrm{CH})}_{\mathrm{x}}$ reveals an oscillatory feature that follows the Stark shift-related first derivative of the material's absorption spectrum that contains $v$(0-1) and $v$(0-2) sidebands of the excited $\mathrm{C}=\mathrm{C}$ stretching vibration that agrees well with the Raman scattering (RS) spectrum. In contrast, the EA spectrum of trans-${(\mathrm{CH})}_{\mathrm{x}}$ does not match the first derivative of the material's absorption spectrum, and the phonon sideband frequency does not agree with the RS spectrum. In addition, the EA spectrum of trans-${(\mathrm{CH})}_{\mathrm{x}}$ reveals a band below the first allowed $1{B}_{\mathrm{u}}$ exciton. We interpret this feature as due to the electric field activated even-parity dark (forbidden) exciton, namely $m{A}_{\mathrm{g}}$ ($m>2$), showing that the ``nonluminescent'' trans-${(\mathrm{CH})}_{\mathrm{x}}$ is due to the reverse order of the excited states, where a series of dark $m{A}_{\mathrm{g}}$ excitons lies below the allowed $1{B}_{\mathrm{u}}$ exciton. This agrees with the unusual phonon sideband in trans-${(\mathrm{CH})}_{\mathrm{x}}$ absorption, since the excited state attenuation caused by the fast internal conversion from $1{B}_{\mathrm{u}}$ to $m{A}_{\mathrm{g}}$ influences the apparent frequency that determines the phonon sideband. Consequently, from the EA and RS spectra we estimate the $1{B}_{\mathrm{u}}$ lifetime in trans-${(\mathrm{CH})}_{\mathrm{x}}$ to be \ensuremath{\sim}30 fs. Moreover, the integrated EA spectrum of trans-${(\mathrm{CH})}_{\mathrm{x}}$ shows a traditional Huang-Rhys type series with a relaxation parameter, $S$ \ensuremath{\sim} 0.5. This indicates that the EA spectrum of the trans isomer is also determined by a Stark shift related to the first derivative of the absorption spectrum, but preferentially for the longest chains in the film's chain lengths distribution. This is due to the ${N}³$ response of the nonlinear susceptibility, ${\ensuremath{\chi}}⁽³⁾$ (\ensuremath{\sim}EA), dependence on the chain length having $N$ monomers.