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arXiv:2006.09004 · Physical review. B./Physical review. B

Excitonic optical spectra and energy structures in a one-dimensional Mott insulator demonstrated by applying a many-body Wannier functions method to a charge model

T. Yamaguchi, Kaoru Iwano, Tatsuya Miyamoto, N. TAKAMURA, N. Kida, Yukihiro Takahashi, Tatsuo Hasegawa, Hiroshi Okamoto

Published Jan 20, 2021• 9 citations
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Abstract

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-${\mathrm{F}}_{2}\mathrm{TCNQ}$ 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.

DOI
10.1103/physrevb.103.045124

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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 propose an effective model called the ``charge model,'' for the half-filled one-dimensional Hubbard and extended Hubbard models. In this model, spin-charge separation, which has been justified from an infinite on-site repulsion (UUU) in the strict sense, is compatible with charge fluctuations. Our analyses based on the many-body Wannier functions succeeded in determining the optical conductivity spectra in large systems. The obtained spectra reproduce the spectra for the original models well even in the intermediate UUU region of U=5U=5U=5--10T10T10T, with TTT being the nearest-neighbor electron hopping energy. These results indicate that the spin-charge separation works fairly well in this intermediate UUU region against the usual expectation and that the charge model is an effective model that applies to actual quasi-one-dimensional materials classified as strongly correlated electron systems.
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.
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 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.
We theoretically study the nonlinear optical response and photoexcited states of the Mott insulators. The nonlinear optical susceptibility ${\ensuremath{\chi}}^{(3)}$ is calculated by using the exact diagonalization technique on small clusters. From the systematic study of the dependence of ${\ensuremath{\chi}}^{(3)}$ on dimensionality, we find that the spin-charge separation plays a crucial role in enhancing ${\ensuremath{\chi}}^{(3)}$ in the one-dimensional (1D) Mott insulators. Based on this result, we propose a holon-doublon model, which describes the nonlinear response in the 1D Mott insulators. These findings show that the spin-charge separation will become a key concept of optoelectronic devices.
We define, compute, and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals (i) mid-gap states related to parity-forbidden optical states and (ii) strong renormalization and hybridization of the excitonic resonance and the absorption band, yielding a Fano resonance. We offer evidence and interpret such a resonance as a signature of nonequilibrium optical excitations resembling excitonic strings, (bi)excitons, and unbound doublon-holon pairs, depending on the magnitude of the intersite Coulomb repulsion. We discuss our results in the context of pump and probe spectroscopy experiments on organic Mott insulators.