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arXiv:2002.01327 · Physical review. B./Physical review. B

Signatures of bosonic excitations in high-harmonic spectra of Mott insulators

Markus Lysne, Yuta Murakami, Philipp Werner

Published May 22, 2020• 29 citations
arXivHTMLPDF

Abstract

The high-harmonic spectrum of the Mott insulating Hubbard model has recently been shown to exhibit plateau structures with cutoff energies determined by $n\mathrm{th}$-nearest-neighbor doublon-holon recombination processes. The spectrum thus allows one to extract the on-site repulsion $U$. Here, we consider generalizations of the single-band Hubbard model and discuss the signatures of bosonic excitations in high-harmonic spectra. Specifically, we study an electron-plasmon model which captures the essential aspects of the dynamically screened Coulomb interaction in solids and a multiorbital Hubbard model with Hund coupling which allows one to analyze the effect of local spin excitations. For the electron-plasmon model, we show that the high-harmonic spectrum can reveal information about the screened and bare on-site interaction, the boson frequency, as well as the relation between boson coupling strength and boson frequency. In the multiorbital case, string states formed by local spin excitations result in an increase of the radiation intensity and cutoff energy associated with higher-order recombination processes.

DOI
10.1103/physrevb.101.195139

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The high-harmonic spectrum of the Mott insulating Hubbard model has recently been shown to exhibit plateau structures with cutoff energies determined by nthn\mathrm{th}nth-nearest-neighbor doublon-holon recombination processes. The spectrum thus allows one to extract the on-site repulsion UUU. Here, we consider generalizations of the single-band Hubbard model and discuss the signatures of bosonic excitations in high-harmonic spectra. Specifically, we study an electron-plasmon model which captures the essential aspects of the dynamically screened Coulomb interaction in solids and a multiorbital Hubbard model with Hund coupling which allows one to analyze the effect of local spin excitations. For the electron-plasmon model, we show that the high-harmonic spectrum can reveal information about the screened and bare on-site interaction, the boson frequency, as well as the relation between boson coupling strength and boson frequency. In the multiorbital case, string states formed by local spin excitations result in an increase of the radiation intensity and cutoff energy associated with higher-order recombination processes.
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Using Floquet dynamical mean-field theory, we study the high-harmonic generation in the time-periodic steady states of wide-gap Mott insulators under ac driving. In the strong-field regime, the harmonic intensity exhibits multiple plateaus, whose cutoff energies ε_{cut}=U+mE_{0} scale with the Coulomb interaction U and the maximum field strength E_{0}. In this regime, the created doublons and holons are localized because of the strong field and the mth plateau originates from the recombination of mth nearest-neighbor doublon-holon pairs. In the weak-field regime, there is only a single plateau in the intensity, which originates from the recombination of itinerant doublons and holons. Here, ε_{cut}=Δ_{gap}+αE_{0}, with Δ_{gap} the band gap and α>1. We demonstrate that the Mott insulator shows a stronger high-harmonic intensity than a semiconductor model with the same dispersion as the Mott insulator, even if the semiconductor bands are broadened by impurity scattering to mimic the incoherent scattering in the Mott insulator.
High-harmonic generation (HHG) in strongly correlated Mott insulators is investigated using exact diagonalization and time-dependent density-matrix propagation of a laser-driven one-dimensional Hubbard chain. By projecting onto equilibrium Hubbard bands, we use the doublon population and its dynamics as a diagnostic to analyze intraband (spin-wave-like) and interband (doublon-holon creation) excitation channels. A filling-dependent crossover emerges: Bloch-like intraband response at dilute filling, mixed dynamics at intermediate filling, and interband-dominated HHG with plateau and cutoff near half filling. In the considered parameter range, increasing interaction strength UUU strongly suppresses interband contributions through the enlarged Mott gap and correlation-induced localization. Intra- and interband current decomposition reveals opposing flows below the Mott gap (Δ_{\mathrm{Mott}}) and selective dephasing suppression of interband coherence, enhancing net doublon accumulation. Time-frequency analysis uncovers the filling-dependent features of quantum trajectories, manifesting in distinct below-Δ_{\mathrm{Mott}} emission. This doublon-based analysis provides a transparent link between equilibrium spin-charge separation and nonequilibrium strong-field response, and clarifies how dephasing modifies interband coherence and doublon accumulation.
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 examine the third-order non-linear optical response of a one-dimensional Mott insulator coupled with phonons. The Mott insulator is described by an extended Hubbard-Holstein model. The third harmonic generation (THG) of the model is calculated by dynamical density-matrix renormalization group. We find that the electron-phonon interaction enhances the intensity of THG if the on-site Coulomb interaction is comparable to the band width, but the enhancement is small for a realistic parameter value of a typical Mott insulator Sr2_22​CuO3_33​. The low-energy spin excitation does not contribute to the optical response if the electron-phonon coupling is neglected. We find that the THG spectrum can detect the spin excitations even for no electron-phonon coupling. The introduction of the electron-phonon coupling leads to a slight increase of low-energy weight in THG without peak structure through phonon-assisted spin excitation. To fully understand the phonon-assisted spin excitation, we additionally calculate the linear susceptibility of a doped Hubbard-Holstein model, showing a spectral distribution different from that at half filling.
High harmonic generation (HHG) has emerged as a powerful probe of ultrafast electron dynamics in solids. However, in strongly correlated materials, where electronic excitations arise from many-body interactions rather than single-particle band dispersion, the field remains in its infancy. Here, we report HHG up to the 23rd^{rd}rd order in the prototypical Mott insulator La2_22​CuO4_44​. We observe a robust 4 eV cutoff that is independent of driving field strength, revealing an intrinsic energy scale defined by the Hubbard bands. Using time-resolved high harmonic spectroscopy, we disentangle the distinct contributions of carrier creation, intraband acceleration, and interband recombination to the nonequilibrium radiation spectrum. We demonstrate that photo-doping triggers a fundamental reorganization of the many-body manifolds above a critical excitation density, a process that renormalizes the band curvature and suppresses nonlinear intraband currents, thereby directly imprinting the signature of many-body band reconstruction onto the harmonic emission. These results establish HHG as a sensitive probe of subtle correlation-driven electronic reconstructions and highlight that many-body interactions enable extreme nonlinear optical responses that are highly tunable in nonequilibrium states.