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arXiv:1809.09800 · Physical review. B./Physical review. B

Floquet spin and spin-orbital Hamiltonians and doublon-holon generations in periodically driven Mott insulators

Kasra Hejazi, Jianpeng Liu, Leon Balents

Published May 9, 2019• 26 citations
arXivHTMLPDF

Abstract

Intense light can alter the electronic properties of materials through its oscillating electric field. The effects on magnetic excitations in insulators, however, are indirect, since these are neutral and do not see the electric field directly. This study reports on how exchange interactions in single- and multiorbital Mott insulators are modified by electromagnetic radiation, whose frequency is assumed to be on the order of the Mott-Hubbard gap. The latter condition results in a nonvanishing creation rate of doubly occupied sites (doublons), which necessitates taking into account the finite bandwidth of the doublon excitations, a feature which goes beyond the na\"{\i}ve leading order strong correlation expansion. This ultimately leads to a complex-valued exchange parameter, where the real part represents the ``Floquet'' spin-exchange interaction, while the imaginary part reflects the creation rate of doublons.

DOI
10.1103/physrevb.99.205111

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Intense light can alter the electronic properties of materials through its oscillating electric field. The effects on magnetic excitations in insulators, however, are indirect, since these are neutral and do not see the electric field directly. This study reports on how exchange interactions in single- and multiorbital Mott insulators are modified by electromagnetic radiation, whose frequency is assumed to be on the order of the Mott-Hubbard gap. The latter condition results in a nonvanishing creation rate of doubly occupied sites (doublons), which necessitates taking into account the finite bandwidth of the doublon excitations, a feature which goes beyond the na"{\i}ve leading order strong correlation expansion. This ultimately leads to a complex-valued exchange parameter, where the real part represents the ``Floquet'' spin-exchange interaction, while the imaginary part reflects the creation rate of doublons.
We consider driving multiorbital Mott insulators using laser radiation. We derive general expressions for periodically driven spin-orbital models using time-dependent perturbation theory in the strong interaction limit. We show that the effective exchange interactions of the Floquet spin-orbital Hamiltonian are highly tunable via variations of the frequency, amplitude, and polarization of the laser. We also take the effect of a finite bandwidth of excitations into account and study possible heating effects. We further apply our formalism to orthorhombic titanates YTiO_{3} and LaTiO_{3} based on first-principles calculations, and we find that the spin exchange interactions in these compounds can be engineered to a large extent by tuning the frequency and electric-field amplitude of the laser.
We demonstrate the existence of long-lived prethermalized states in the Mott insulating Hubbard model driven by periodic electric fields. These states, which also exist in the resonantly driven case with a large density of photo-induced doublons and holons, are characterized by a nonzero current and an effective temperature of the doublons and holons which depends sensitively on the driving condition. Focusing on the specific case of resonantly driven models whose effective time-independent Hamiltonian in the high-frequency driving limit corresponds to noninteracting fermions, we show that the time evolution of the double occupation can be reproduced by the effective Hamiltonian, and that the prethermalization plateaus at finite driving frequency are controlled by the next-to-leading–order correction in the high-frequency expansion of the effective Hamiltonian. We propose a numerical procedure to determine an effective Hubbard interaction that mimics the correlation effects induced by these higher-order terms.
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.
We present a scheme to control the spin-exchange interactions by manipulating the orbital degrees of freedom using a periodic drive. We discuss two different protocols for orbital Floquet engineering. In one case, a periodic drive modifies the properties of the ligand orbitals which mediate magnetic interactions between transition-metal ions. In the other case, we consider drive-induced mixing of ddd orbitals on each magnetic ion. We first find that an AC Stark shift of orbitals induces a change comparable to that induced from photoinduced hopping schemes, but expands the applicable frequency ranges. Next, we find that radiatively induced coherent vibrations provide a realistic path for Floquet orbital engineering with short pulses of electric fields weaker than 0.5 V/\AA{} producing 55%--10%5 changes in the magnetic coupling of Mott insulators such as the rare-earth titanates.
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 study the photoinduced breakdown of a two-orbital Mott insulator and resulting metallic state. Using time-dependent density matrix renormalization group, we scrutinize the real-time dynamics of the half-filled two-orbital Hubbard model interacting with a resonant radiation field pulse. The breakdown, caused by production of doublon-holon pairs, is enhanced by Hund's exchange, which dynamically activates large orbital fluctuations. The melting of the Mott insulator is accompanied by a high to low spin transition with a concomitant reduction of antiferromagnetic spin fluctuations. Most notably, the overall time response is driven by the photogeneration of excitons with orbital character that are stabilized by Hund's coupling. These unconventional ``Hund excitons'' correspond to bound spin-singlet orbital-triplet doublon-holon pairs. We study exciton properties such as bandwidth, binding potential, and size within a semiclassical approach. The photometallic state results from a coexistence of Hund excitons and doublon-holon plasma.