Linear and nonlinear optical properties of one-dimensional Mott insulators consisting ofNi-halogen chain andCuO-chain compounds

Abstract

We studied the linear and nonlinear optical responses in the one-dimensional (1D) Mott insulators of the halogen $(X)$-bridged nickel compounds (the $\mathrm{Ni}X$-chain compounds), $[{\mathrm{Ni}(\mathrm{chxn})}_{2}X]$${Y}_{2}$ [$X,Y=\mathrm{Cl}$; $X,Y=\mathrm{Br}$; $X=\mathrm{Cl}$, $Y={\mathrm{NO}}_{3}$: (chxn)=cyclohexanediamine] and the copper oxide $(\mathrm{CuO})$ chain compounds, ${A}_{2}{\mathrm{CuO}}_{3}$ ($A=\mathrm{Sr}$ and $\mathrm{Ca}$). The excitation profiles of the photoconductivity as well as the photoluminescence efficiency measurements show that charge-transfer (CT) excited states in the $\mathrm{Ni}X$-chain compounds form excitonic bound states, while the excitonic effect is relatively small in ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ and negligible in ${\mathrm{Ca}}_{2}{\mathrm{CuO}}_{3}$. The relatively large excitonic effect in the $\mathrm{Ni}X$-chain compounds is attributable to the strong 1D confinement of the electronic states. The temperature dependence of the ${\ensuremath{\epsilon}}_{2}$ spectra reveals that the spectral widths ${\ensuremath{\Gamma}}_{\mathrm{CT}}$ of the CT bands are dominated mainly by the electron--lattice interaction, which is smaller in the $\mathrm{Ni}X$-chain compounds than in the $\mathrm{CuO}$-chain ones. The ${\ensuremath{\chi}}^{(3)}(\ensuremath{-}\ensuremath{\omega};0,0,\ensuremath{\omega})$ spectra of the 1D Mott insulators were obtained by the electroreflectance spectroscopy. The maximum values of $\ensuremath{\mid}\mathrm{Im}{\ensuremath{\chi}}^{(3)}(\ensuremath{-}\ensuremath{\omega};0,0,\ensuremath{\omega})\ensuremath{\mid}$ in the 1D Mott insulators$(\ensuremath{\sim}{10}^{\ensuremath{-}5}--{10}^{\ensuremath{-}8}\phantom{\rule{0.3em}{0ex}}\mathrm{esu})$ were considerably larger than those in other 1D semiconductors such as 1D band insulators of silicon polymers, and 1D Peierls insulators of $\ensuremath{\pi}$-conjugated polymers and halogen-bridged Pt compounds $(\ensuremath{\sim}{10}^{\ensuremath{-}8}--{10}^{\ensuremath{-}10}\phantom{\rule{0.3em}{0ex}}\mathrm{esu})$. To elucidate the enhancement of $\ensuremath{\mid}\mathrm{Im}{\ensuremath{\chi}}^{(3)}(\ensuremath{-}\ensuremath{\omega};0,0,\ensuremath{\omega})\ensuremath{\mid}$ in the 1D Mott insulators, we have compared the nature of the photoexcited states of the 1D Mott insulators with those of the 1D band and Peierls insulators. In the 1D Mott insulators, the odd and even CT excited states are nearly degenerate. This degeneracy induces the large transition dipole moment between these two states and then leads to the enhancement of ${\ensuremath{\chi}}^{(3)}$. Such a feature in the 1D Mott insulators is independent of the magnitude of the excitonic effect, although the excitonic effect sharpens the ${\ensuremath{\chi}}^{(3)}$ spectrum and enhances the maximum value of $\ensuremath{\mid}{\ensuremath{\chi}}^{(3)}\ensuremath{\mid}$. In the 1D band and Peierls insulators, on the other hand, the splitting between the lowest excited state with odd parity and the second-lowest one with even parity is as large as the exciton binding energy. It leads to the diminution of the transition dipole moment between these two excited states and hence of ${\ensuremath{\chi}}^{(3)}$. These differences of the photoexcited states between the 1D Mott insulators and others have been explained in terms of the 1D extended Peierls--Hubbard model.