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Physical review. B./Physical review. B

Ultrabosonic behavior in photoexcited one-dimensional Mott insulators in the region of weak intersite Coulomb interaction

Kaoru Iwano, T. Yamaguchi, Hiroshi Okamoto

Published Dec 10, 2020• 2 citations
Publisher

Abstract

This paper reports a unique behavior expected for the optical excitations in one-dimensional Mott insulators. When the intersite Coulombic attraction does not work between two elementary charge excitations, i.e., a doublon and a holon, the lowest optical excitations are described as an unbound pair of them, still having finite mutual correlation due to the forbidden double occupancy on the same site. We find that, in such a situation, the pairs obey a particle statistics that exceeds that of ordinary bosons. This feature appears most directly in the enhancement factor of the matrix element for the pair photocreation. We discuss the possible mechanism for this ultrabosonic behavior and also demonstrate that this behavior is maintained even if we include a small amount of interiste Coulomibic interaction. Lastly, this enhancement factor almost coincides with that for ordinary bosons when the degree of the intersite interaction exceeds a certain value that switches on the formation of a bound doublon-holon pair.

DOI
10.1103/physrevb.102.245114

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No author provided

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This paper reports a unique behavior expected for the optical excitations in one-dimensional Mott insulators. When the intersite Coulombic attraction does not work between two elementary charge excitations, i.e., a doublon and a holon, the lowest optical excitations are described as an unbound pair of them, still having finite mutual correlation due to the forbidden double occupancy on the same site. We find that, in such a situation, the pairs obey a particle statistics that exceeds that of ordinary bosons. This feature appears most directly in the enhancement factor of the matrix element for the pair photocreation. We discuss the possible mechanism for this ultrabosonic behavior and also demonstrate that this behavior is maintained even if we include a small amount of interiste Coulomibic interaction. Lastly, this enhancement factor almost coincides with that for ordinary bosons when the degree of the intersite interaction exceeds a certain value that switches on the formation of a bound doublon-holon pair.
We revisit the holon-doublon binding problem in two-dimensional (2D) photoexcited Mott insulators. Low-energy photoexcited states in Mott insulators are described as a pair state of a doublon and a holon. The most basic question is whether its bound state is formed in the lowest-energy state, and negative and positive responses have been discussed in the past. In this study we begin with the 2D Hubbard model, and transform it into the first effective model, which is based on the t/Ut/Ut/U expansion, with UUU and ttt being the Hubbard UUU and the electron hopping energy, respectively. We find that quantitative reliability is assured for $U/t\ensuremath{\gtrsim}10$. Furthermore, we transform it into a second effective model that selects essential states in the low-energy region. In both effective models we distinguish two magnetic terms, namely, the spin-exchange interaction and the three-site transfer, and parametrize the two terms with the parameters Jex{J}_{\mathrm{ex}}Jex​ and J3site{J}_{3\mathrm{site}}J3site​. By changing the parameters apart from the restriction given by the Hubbard model, any positive Jex{J}_{\mathrm{ex}}Jex​ value with J3site=0{J}_{3\mathrm{site}}=0J3site​=0 yields a finite amount of binding, whereas a finite value of J3site{J}_{3\mathrm{site}}J3site​ suppresses the binding significantly, still leaving the Hubbard case of U=10tU=10tU=10t in the vicinity of the bound-unbound boundary.
We investigate the effect of nonlocal interactions on the photodoped Mott insulating state of the two-dimensional Hubbard model using a nonequilibrium generalization of the dynamical cluster approximation. In particular, we compare the situation where the excitonic states are lying within the continuum of doublon-holon excitations to a setup where the excitons appear within the Mott gap. In the first case, the creation of nearest-neighbor doublon-holon pairs by excitations across the Mott gap results in enhanced excitonic correlations, but these excitons quickly decay into uncorrelated doublons and holons. In the second case, photoexcitation results in long-lived excitonic states. While in a low-temperature equilibrium state, excitonic features are usually not evident in single-particle observables such as the photoemission spectrum, we show that the photoexcited nonequilibrium system can exhibit in-gap states associated with the excitons. The comparison with exact-diagonalization results for small clusters allows us to identify the signatures of the excitons in the photoemission spectrum.
We theoretically investigate the relaxation of photogenerated charge carriers in one-dimensional Mott insulators. We adopt the Pariser–Parr–Pople model, and numerically calculate the time development of the nonequilibrium state excited by a weak light pulse. We investigate the dependence of the dynamics on the Coulomb correlation strength in the case where the binding effect between photogenerated opposite charges is significant. In the strong-correlation region (U≫WU \gg WU≫W), where U is the onsite Coulomb interaction energy and W is the bandwidth, the Auger recombination where two bound holon–doublon pairs decay into one unbound holon–doublon pair dominates the decay dynamics. From the strong- to intermediate (U≃WU \simeq WU≃W)-correlation regions, the Auger recombination is always dominant, but the charge carriers involved in the process cannot be described by a holon and a doublon in the intermediate-correlation region. In the crossover region between these two regions, the Auger coefficient is strongly enhanced, and the decay time constant is consistent with those obtained in recent experiments.
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.
We study the nondegenerate one-dimensional two-orbital Hubbard model with an interorbital Coulomb interaction. By means of the density-matrix renormalization group technique, we calculate the local single-particle density of states and the optical conductivity at zero temperature. We find that a finite interorbital Coulomb repulsion VVV generates a different class of states within the Mott-Hubbard band which has a large weight of holon-doublon pairs, which we hence call the holon-doublon band (HDB). When VVV is sufficiently large, the HDB specifies the gapless low-energy excitations, and the system becomes an unconventional correlated metal. Optical conductivity results resolve different metallic behaviors for zero and finite interaction VVV. Compared to the case without an interorbital interaction, the conductivity is strongly reduced in the correlated holon-doublon metal for finite VVV. In addition, the absorption spectrum is dominated by the HDB, which is clearly distinguishable from the Mott-Hubbard band.
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.