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arXiv:1211.3236 · Physical Review Letters

Ultrafast Charge Recombination in a Photoexcited Mott-Hubbard Insulator

Zala Lenarčič, Peter Prelovšek

Published Jul 2, 2013• 96 citations
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Abstract

We present a calculation of the recombination rate of the excited holon-doublon pairs based on the two-dimensional model relevant for undoped cuprates, which shows that fast processes, observed in pump-probe experiments on Mott-Hubbard insulators in the picosecond range, can be explained even quantitatively with the multimagnon emission. The precondition is the existence of the Mott-Hubbard bound exciton of the s-type. We find that its decay is exponentially dependent on the Mott-Hubbard gap and on the magnon energy, with a small prefactor, which can be traced back to strong correlations and consequently large exciton-magnon coupling.

DOI
10.1103/physrevlett.111.016401

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We present a calculation of the recombination rate of the excited holon-doublon pairs based on the two-dimensional model relevant for undoped cuprates, which shows that fast processes, observed in pump-probe experiments on Mott-Hubbard insulators in the picosecond range, can be explained even quantitatively with the multimagnon emission. The precondition is the existence of the Mott-Hubbard bound exciton of the s-type. We find that its decay is exponentially dependent on the Mott-Hubbard gap and on the magnon energy, with a small prefactor, which can be traced back to strong correlations and consequently large exciton-magnon coupling.
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We theoretically investigate the dynamics of photoexcited states 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 light pulse. In the weaker light excitation case where the maximum photoexcitation density is below about 18%, the charge carriers in the photoexcited states are holons and doublons, and the geminate recombination of bound doublon–holon pairs, namely, the Auger recombination process dominates the decay of the photogenerated holons and doublons with the realistic Coulomb parameters. In the stronger light excitation case where the density is above the value, the charge carriers of the photoexcited states cannot be described by holons and doublons. As a result, the Auger recombination process of doublon–holon pairs is not the main decay route of the photogenerated charges. Furthermore, the spin and the charge degrees of freedom are coupled, and spin relaxation occurs in the photoexcited states. As the density of the photogenerated charge carriers becomes larger, the decay time decreases. This tendency is consistent with experiments.
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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 theoretically investigate pump-probe optical responses in the two-dimensional extended Hubbard model describing cuprates by using a time-dependent Lanczos method. At half filling, pumping generates photoinduced absorptions inside the Mott gap. A part of low-energy absorptions is attributed to the independent propagation of photoinduced holons and doublons. The spectral weight just below the Mott gap increases with decreasing the on-site Coulomb interaction UUU. We find that the next-nearest-neighbor Coulomb interaction V1{V}_{1}V1​ enhances this UUU dependence, indicating the presence of biexcitonic contributions formed by two holon-doublon pairs. Photopumping in hole-doped systems also induces spectral weights below remnant Mott-gap excitations, being consistent with recent experiments. The induced weights are less sensitive to V1{V}_{1}V1​ and may be related to the formation of a biexcitonic state in the presence of hole carriers.