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arXiv:1409.2347 · Physical Review B

Charge recombination in undoped cuprates

Zala Lenarčič, Peter Prelovšek

Published Dec 22, 2014• 46 citations
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Abstract

We theoretically analyze the process of charge recombination in the planar Mott-Hubbard insulators with the aim to explain the short picosecond-range lifetimes of photoexcited carriers, experimentally studied via pump-probe experiments on the undoped cuprates. The recombination mechanism consists of two essential ingredients: the formation of a metastable $s$-type bound holon-doublon pair, i.e., the Mott exciton, and the decay of such an excitonic state via the multimagnon emission. In spite of the large gap that requires many bosons to be emitted, the latter process is fast due to a large exchange scale and strong charge-spin coupling in planar systems. As the starting microscopic model we consider the single-band Hubbard model and then a more realistic three-band model for cuprates, both leading to the same minimal one. The decay rate of the exciton is evaluated numerically via the Fermi golden rule, having consistency also with the direct time-evolution calculation. The decay rate reveals exponential dependence on the ratio of the Mott-Hubbard gap and the exchange coupling, the result qualitatively reproduced also within a toy exciton-boson model.

DOI
10.1103/physrevb.90.235136

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We theoretically analyze the process of charge recombination in the planar Mott-Hubbard insulators with the aim to explain the short picosecond-range lifetimes of photoexcited carriers, experimentally studied via pump-probe experiments on the undoped cuprates. The recombination mechanism consists of two essential ingredients: the formation of a metastable sss-type bound holon-doublon pair, i.e., the Mott exciton, and the decay of such an excitonic state via the multimagnon emission. In spite of the large gap that requires many bosons to be emitted, the latter process is fast due to a large exchange scale and strong charge-spin coupling in planar systems. As the starting microscopic model we consider the single-band Hubbard model and then a more realistic three-band model for cuprates, both leading to the same minimal one. The decay rate of the exciton is evaluated numerically via the Fermi golden rule, having consistency also with the direct time-evolution calculation. The decay rate reveals exponential dependence on the ratio of the Mott-Hubbard gap and the exchange coupling, the result qualitatively reproduced also within a toy exciton-boson model.
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.
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.
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.
Motivated by recent experiments on Mott insulators, in both iridates and ultracold atoms, we theoretically study the effects of magnetic order on the Mott-Hubbard excitons. In particular, we focus on spin-mediated doublon-holon pairing in Hubbard materials. We use several complementary theoretical techniques: Mean-field theory to describe the spin degrees of freedom, the self-consistent Born approximation to characterize individual charge excitations across the Hubbard gap, and the Bethe-Salpeter equation to identify bound states of doublons and holons. The binding energy of the Mott exciton is found to increase with increasing the N\'eel order parameter, whereas the exciton mass decreases. We observe that these trends rely significantly on the retardation of the effective interaction, and require consideration of multiple effects from changing the magnetic order. Our results are consistent with the key qualitative trends observed in recent experiments on iridates. Moreover, the findings could have direct implications on ultracold atom Mott insulators where the Hubbard model is the exact description of the system and the microscopic degrees of freedom can be directly accessed.
Charge creation via quantum tunneling, i.e. dielectric breakdown, is one of the most fundamental and significant phenomena arising from strong light(field)-matter coupling. In this work, we conduct a systematic numerical analysis of quantum tunneling in one-dimensional Mott insulators described by the extended (UUU-VVV) Hubbard model. We discuss the applicability of the analytical formula for doublon-holon (DH) pair production, previously derived for the one-dimensional Hubbard model, which highlights the relationship between the tunneling threshold, the charge gap, and the correlation length. We test the formulas ability to predict both DH pair production and energy increase rate. Using tensor-network-based approaches, we demonstrate that the formula provides accurate predictions in the absence of excitonic states facilitated by the nearest-neighbor interaction VVV. However, when excitonic states emerge, the formula more accurately describes the rate of energy increase than the DH pair creation rate and in both cases gets improved by incorporating the exciton energy as the effective gap.
Resonant interactions associated with the emergence of a bound state constitute one of the cornerstones of modern many-body physics, ranging from Kondo physics, BEC-BCS crossover, to tunable interactions at Feshbach resonances in ultracold atoms or 2D semiconductors. Here we present a Feshbach perspective on the origin of strong pairing in Fermi-Hubbard type models. We perform a theoretical analysis of interactions between charge carriers in doped Mott insulators, modeled by a near-resonant two-channel scattering problem, and find strong evidence for Feshbach-type interactions in the dx2−y2d_{x^2-y^2}dx2−y2​ channel that can support strong pairing, consistent with the established phenomenology of cuprates. Existing experimental and numerical results on hole-doped cuprates lead us to conjecture the existence of a light, long-lived, low-energy excited state of two holes with bipolaron character in these systems, which enables near-resonant interactions and can thus provide a microscopic foundation for theories of high-temperature superconductivity involving strong attraction, as assumed e.g. in BEC-BCS crossover scenarios. To put our theory to a direct test we suggest to use coincidence angle-resolved photoemission spectroscopy (cARPES), pair-tunneling measurements or less direct pump-probe experiments. The emergent Feshbach resonance we propose could also underlie superconductivity in other doped antiferromagnetic Mott insulators, as recently proposed for bilayer nickelates, highlighting its potential as a unifying strong-coupling pairing mechanism rooted in quantum magnetism.