Correlations drive the attosecond response of strongly-correlated insulators

Technical Summary: Correlations Drive the Attosecond Response of Strongly-Correlated Insulators

Problem Statement
Attosecond spectroscopy has successfully elucidated light-driven coherent electron dynamics in weakly-correlated materials, such as band insulators and semiconductors. However, the behavior of strongly-correlated systems at sub- to few-femtosecond timescales remains largely unknown, despite this being the natural regime for electron-electron interactions. Standard theoretical descriptions often rely on single-particle pictures or simplified few-band models (e.g., the Dynamical Franz-Keldysh Effect), which are expected to break down when many-body processes dominate. A critical open question is whether electronic correlations amplify sub-optical-cycle dynamics or suppress the ultrafast response through enhanced electromagnetic field screening. Furthermore, while the Hubbard $U$ parameter (quantifying on-site Coulomb repulsion) is central to correlated systems, its light-driven renormalization has not been directly measured at its intrinsic timescale.

Methodology
The authors employed attosecond-resolved pump-probe transient reflectivity experiments to compare a prototypical band insulator (Magnesium Oxide, MgO) with a strongly-correlated insulator (Nickel Oxide, NiO) under identical conditions.

• Experimental Setup: A 5 fs, p-polarized pump pulse (1.58 eV, 6 TW cm$^{-2}$) excited the samples. A broadband attosecond probe pulse (40–72 eV) measured the transient reflectivity with a temporal stability of 100 as. The probe specifically targeted the Mg $L_{2,3}$ and Ni $M_{2,3}$ edges.
• Theoretical Framework: The experimental data were interpreted using state-of-the-art ab initio time-dependent density functional theory plus Hubbard $U$ (TDDFT+$U$) calculations coupled to macroscopic Maxwell equations. These simulations included all necessary core levels and treated the system as a bulk antiferromagnet. Additionally, multiplet ligand-field calculations were used to identify the specific local parameters (Hubbard $U$, charge-transfer energy, and hybridization) governing the spectral shifts.

Key Results

1. Fundamentally Different Responses:

   • MgO (Band Insulator): Exhibited a large reflectivity change ($\approx$20%) localized around the pump-probe overlap, characterized by oscillations with a 1.3 fs period (half the driving field period). This behavior is consistent with the Dynamical Franz-Keldysh Effect (DFKE), described by field-induced modifications of the single-particle band structure.
   • NiO (Correlated Insulator): Showed a much weaker reflectivity change ($\approx$4%) that rose more slowly and persisted long after excitation. Crucially, no field-driven oscillations were resolved during the pump pulse. The spectral response was not a complex broadening or new band formation but a pure rigid redshift of the absorption edge.

2. Light-Driven Quench of Correlations:

   • The absence of DFKE-like oscillations and the presence of a pure redshift in NiO indicate that single-particle pictures fail.
   • TDDFT+$U$ simulations revealed that the experimental signal is reproduced only when the Hubbard $U$ is allowed to evolve dynamically. When $U$ was "frozen" to its ground-state value, the transient signal almost entirely disappeared.
   • Multiplet calculations confirmed that the observed redshift requires a simultaneous renormalization of the Hubbard $U$ (reduced by $\approx$100 meV) and a reduction in Ni–O hybridization strength.

3. Timescale of $U$ Renormalization:

   • The experiment measured the temporal evolution of the Hubbard parameter, $\Delta U(t)$.
   • While TDDFT+$U$ (using an adiabatic approximation) predicted an instantaneous response limited only by the laser pulse duration, the experimental data revealed an intrinsic response time of $(13.3 \pm 1.0)$ fs.
   • This delay is attributed to the finite time required for the electronic system to react to the light-induced change in screening, a degree of freedom not captured by the adiabatic functional used in the simulations.

4. Long-Lived Dynamics:

   • Beyond 40 fs, the response deviated from a pure redshift, showing a blue shift and new features associated with charge-transfer excitations and the formation of a small polaron.
   • The system settled into a metastable, structurally distorted non-thermal lattice state that persisted for at least 50 ps, demonstrating that strong correlations can lead to thermalization bottlenecks.

Significance and Claims
The paper claims to provide the first direct experimental measurement of Hubbard $U$ renormalization in a strongly-correlated material (NiO) at its natural timescale. Key contributions include:

• Demonstrating a new mechanism: The response of strongly-correlated solids to intense light fields is governed by a laser-driven quench of electron correlations rather than field-driven band structure modifications.
• Defining a new observable: The few-femtosecond response time of the Hubbard $U$ represents a new observable linked to the inherent speed at which electron-electron interactions (or screening) can be manipulated by a laser pulse.
• Benchmarking Theory: The discrepancy between the instantaneous theoretical response and the measured 13.3 fs delay highlights a limitation in current adiabatic approximations for TDDFT+$U$, setting a challenging benchmark for future ab initio theories to capture non-instantaneous electronic responses in correlated systems.
• Clarifying Light-Matter Interaction: The work establishes that in strongly-correlated systems, the Hubbard $U$ renormalization is driven by laser intensity rather than the electric field phase (Carrier Envelope Phase), contrasting with control mechanisms in standard insulators.

The authors conclude that this work sheds light on the entire light-induced response of strongly-correlated systems, from the sub-femtosecond electronic quench to the picosecond formation of metastable non-thermal states.