Optical Spectra and Exciton in Correlated Insulators in Electron–Hole Systems

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We study the optical properties of an electron–hole two-band Hubbard model with interactions of electron–electron (hole–hole) repulsion $U$ and electron–hole attraction $U'$. In the case of two types of correlated insulators at half filling, viz., the Mott–Hubbard type and the biexciton type, interband linear absorption/gain spectra including excitonic effects are calculated analytically using two-site dynamical mean-field theory and ladder approximation. We show that an exciton-like peak structure emerges because of an “exciton” in the sea of correlated fermions when $U'$ is larger than a certain critical value. The binding energy of the photoinduced excitonic bound state and the spectral intensity are evaluated as a function of $U'$. The emergence and absence of the exciton-like peak suggests that there are two different insulating mechanisms in the Mott–Hubbard insulating state of the electron–hole system: one is attributable to only $U$ and the other is attributable to both $U$ and $U'$; the latter is called the excitonic Mott–Hubbard insulating state. The intrinsic difference of the mechanisms cannot be captured from only single-particle properties such as the density of states, but it appears clearly in optical properties reflecting two-particle correlations.
2010-10-15