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arXiv:cond-mat/0312625 · Physical Review B

Temperature and dimensionality dependencies of optical absorption spectra in Mott insulators

H. Onodera, Takami Tohyama, Sadamichi Maekawa

Published Jun 28, 2004• 9 citations
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Abstract

We investigate the temperature dependence of optical absorption spectra of one-dimensional (1D) and two-dimensional (2D) Mott insulators by using an effective model in the strong-coupling limit of a half-filled Hubbard model. In the numerically exact diagonalization calculations on finite-size clusters, we find that in 1D the energy position of the absorption edge is almost independent of temperature, while in 2D the edge position shifts to lower energy with increasing temperature. The different temperature dependence between 1D and 2D is attributed to the difference of the coupling of the charge and spin degrees of freedom. The implications of the results on experiments are discussed in terms of the dimensionality dependence.

DOI
10.1103/physrevb.69.245117

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We investigate the temperature dependence of optical absorption spectra of one-dimensional (1D) and two-dimensional (2D) Mott insulators by using an effective model in the strong-coupling limit of a half-filled Hubbard model. In the numerically exact diagonalization calculations on finite-size clusters, we find that in 1D the energy position of the absorption edge is almost independent of temperature, while in 2D the edge position shifts to lower energy with increasing temperature. The different temperature dependence between 1D and 2D is attributed to the difference of the coupling of the charge and spin degrees of freedom. The implications of the results on experiments are discussed in terms of the dimensionality dependence.
We theoretically investigate the light absorption spectrum of two-dimensional (2D) Mott insulators. We employ the numerical diagonalization method to calculate the light absorption spectrum with using the effective Hamiltonian for the extended Hubbard model, which is valid when the on-site Coulomb interaction energy UUU is much larger than the nearest-neighbor transfer integral ttt and the nearest-neighbor Coulomb interaction energy VVV. For V=0V=0V=0, the absorption spectrum consists of a broad band with a width of about 16t16t16t and a sharp central peak, and the energy eigenstates contributing to the absorption spectrum do not have the antiferromagnetic (AF) spin order, when UUU is sufficiently larger than ttt. These features result from the spin-charge interplay inherent in the very strong correlation region where charge transfer term is dominant. With decreasing U∕tU∕tU∕t, the peak structure in absorption spectrum becomes unclear and some low energy eigenstates have the AF spin order, as a result of the spin-spin interaction term. For large V∕tV∕tV∕t, the dominant peak arises in the lower energy region of the spectrum. A large number of holon-doublon bound states, which have nearly the same charge but different spin structures, are responsible for this peak, in contrast to the conventional exciton state. This is also in contrast to the charge bound states in one-dimensional (1D) Mott insulators, where a single energy eigenstate dominates the optical transition moment as a result of the spin-charge separation. The essentially different absorption spectra between the 1D and 2D Mott insulators originate from the difference in the coupling between spin and charge degrees of freedom.
We applied a many-body Wannier functions method to theoretically calculate the excitonic optical conductivity spectrum and energy structure in a one-dimensional (1D) Mott insulator at absolute zero temperature with a large system size. Focusing on full charge fluctuations associated with holon and doublon pairs, we employ a charge model, which is interpreted as an effective model for investigating the photoexcitations of a 1D extended Hubbard model under a half-filling of the spin-charge separation. As a result, theoretical spectra with the appropriate broadenings qualitatively reproduce the recent experimental data of ET-F2TCNQ{\mathrm{F}}_{2}\mathrm{TCNQ}F2​TCNQ at 294 K with and without a modulated electric field. Regarding the excitonic energy structure, we found that the excitons, particularly for even-parity, are weakly bound by many-body effects. This is also consistent with the fitting parameters reported in a recent experiment. Thus, the theoretical method presented in this paper is useful for understanding the physical roles of the charge fluctuations in many-body excited states of a 1D Mott insulator.
We study the third-order nonlinear optical susceptibility ${\ensuremath{\chi}}^{(3)}$ and photoexcited states of two-dimensional (2D) Mott insulators by using an effective model in the strong-coupling limit of a half-filled Hubbard model. In the numerically exact diagonalization calculations on finite-size clusters, we find that the coupling of charge and spin degrees of freedom plays a crucial role in the distribution of the dipole-allowed states with odd parity and the dipole-forbidden states with even parity in the photoexcited states. This is in contrast with the photoexcited states in one dimension, where the charge and spin degrees of freedom are decoupled. In the third-harmonic generation (THG) spectrum, the main contribution is found to come from the process of three-photon resonance associated with the odd-parity states. As a result, the two-photon resonance process is less pronounced in the THG spectrum. The calculated THG spectrum is compared with recent experimental data. We also find that ${\ensuremath{\chi}}^{(3)}$ with a cross-polarized configuration of pump and probe photons shows spectral distributions similar to ${\ensuremath{\chi}}^{(3)}$ with a copolarized configuration, although the weight is small. These findings will help analyses of the experimental data of ${\ensuremath{\chi}}^{(3)}$ in 2D Mott insulators.
We have made an angle-resolved photoemission study of a one-dimensional Mott-Hubbard insulator Na0.96V2O5{\mathrm{Na}}_{0.96}{\mathrm{V}}_{2}{\mathrm{O}}_{5}Na0.96​V2​O5​ and found that the spectra of the V 3d3d3d lower Hubbard band are strongly dependent on the temperature. We have calculated the one-particle spectral function of the one-dimensional $t\ensuremath{-}J$ model at finite temperatures by exact diagonalization and compared them with the experimental results. Good overall agreement is obtained between experiment and theory. The strong finite temperature effects are discussed in terms of the existence of the ``Fermi surface'' of the spinon band.
We investigate the resonant two-magnon Raman scattering in two-dimensional (2D) Mott insulators by using a half-filled 2D Hubbard model in the strong coupling limit. By performing numerical diagonalization calculations for small clusters, we find that the Raman intensity is enhanced when the incoming photon energy is not near the optical absorption edge but well above it, being consistent with experimental data. The absence of resonance near the gap edge is associated with the presence of background spins, while photoexcited states for resonance are found to be characterized by the charge degree of freedom. The resonance mechanism is different from those proposed previously.
We employ dynamical density-matrix renormalization-group (DDMRG) and field-theory methods to determine the frequency-dependent optical conductivity in one-dimensional extended, half-filled Hubbard models. The field-theory approach is applicable to the regime of ``small'' Mott gaps which is the most difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers analytical results obtained previously by means of strong-coupling techniques. We focus on exciton formation at energies below the onset of the absorption continuum. As a consequence of spin-charge separation, these Mott-Hubbard excitons are bound states of spinless, charged excitations (``holon-antiholon'' pairs). We also determine exciton binding energies and sizes. In contrast to simple band insulators, we observe that excitons exist in the Mott-insulating phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore, our results show that the exciton binding energy and size are not related in a simple way to the strength of the Coulomb interaction.