Terahertz harmonic generation across the Mott insulator-metal transition

Technical Summary: Terahertz Harmonic Generation across the Mott Insulator-Metal Transition

Problem Statement
High harmonic generation (HHG) is a well-established probe for electronic structures in atoms, molecules, and solids, primarily in the optical (visible/ultraviolet) regime. While recent advances have enabled Terahertz (THz) HHG studies in Dirac and topological materials, the behavior of HHG in strongly correlated systems, specifically Mott insulators, remains largely unexplored both theoretically and experimentally. Key open questions include:

1. Can Mott insulators exhibit THz HHG despite the THz photon energy (few meV) being orders of magnitude smaller than the Mott gap (~1 eV)?
2. What are the underlying mechanisms for THz HHG in different phases (insulating vs. metallic) of correlated materials?
3. Do higher-order THz harmonics exhibit anomalous temperature dependencies similar to those observed in mid-infrared (MIR) excitation of Mott insulators like Ca$_2$RuO$_4$?
4. How does the HHG response behave in the vicinity of the Mott insulator-metal transition (IMT)?

Methodology
The study employs a combination of experimental measurements and theoretical modeling:

• Experimental Setup:

  • Samples: High-quality thin films of rare-earth nickelates (RNiO$_3$), specifically LaNiO$_3$ (a paramagnetic metal) and NdNiO$_3$ (exhibiting a phase diagram with paramagnetic metal, paramagnetic insulator, and antiferromagnetic insulator phases), were grown on LaAlO$_3$ and LSAT substrates.
  • Excitation: Intense, narrowband, multicycle THz pulses with a central frequency of $\omega = 0.3$ THz and electric field strength $E_{THz} \sim 100$ kV/cm were used to drive the samples.
  • Detection: Transmitted radiation was filtered through two bandpass filters centered at $3\omega = 0.9$ THz to isolate the third harmonic generation (THG) signal. The signal was detected in the time domain using a 2 mm ZnTe crystal.
  • Characterization: Temperature-dependent resistivity measurements were conducted to identify phase transitions ($T_{IMT}$ and $T_N$). THG intensity was measured as a function of temperature, fundamental THz intensity, and polarization angle.

• Theoretical Modeling:

  • Frameworks: The authors utilized the nonequilibrium Dynamical Mean-Field Theory (DMFT) formalism.
  • Models:
    • A two-orbital Hubbard model was used to simulate the AFM insulating and PM insulating phases, accounting for spin-charge and orbital-charge couplings.
    • A single-orbital Hubbard model was employed for the high-temperature PM metallic phase to describe intraband dynamics of renormalized quasiparticles.
  • Simulation Details: Simulations used the NESSi library with non-crossing approximation (NCA) and one-crossing approximation (OCA) impurity solvers to analyze current dynamics $J(t)$ driven by electric field pulses $E(t)$. The HHG spectrum was derived from the Fourier transform of the current.

Key Results

1. Observation of THz THG: Clear THG signals were observed in all three electronic regimes of the nickelates: the low-temperature antiferromagnetic (AFM) insulating phase, the intermediate paramagnetic (PM) insulating phase, and the high-temperature PM metallic phase.
2. Distinct Temperature Dependencies:
   • AFM Insulating Phase: The THG intensity increases monotonously and sharply upon cooling below the Néel temperature ($T_N$), showing an enhancement of more than one order of magnitude at $\sim 5$ K compared to $T_N$.
   • PM Metallic Phase: The THG intensity also increases upon cooling, consistent with the behavior of heavy quasiparticles.
   • PM Insulating Phase (Intermediate): In contrast to the other phases, the THG intensity decreases upon cooling in the intermediate PM insulating regime (between $T_{IMT}$ and $T_N$).
3. Non-Perturbative Regime: The THG intensity scales with the fundamental intensity as $I_{3\omega} \propto I_{\omega}^{2.42-2.68}$, indicating that the emission originates from the non-perturbative light-matter interaction regime rather than a simple cubic perturbative response.
4. Isotropic Response: Polarization-dependent measurements revealed that the THG signal is isotropic with respect to the driving THz field polarization, attributed to the isotropic strain of the cubic substrates.
5. Theoretical Reproduction: The DMFT simulations successfully reproduced the experimental trends:
   • In the AFM phase, the enhancement is attributed to strong spin-charge and orbital-charge couplings. As temperature drops, thermal fluctuations in the spin background are suppressed, increasing coherence between doublons and holons, reducing phase cancellations, and enhancing harmonic intensity.
   • In the PM metallic phase, the enhancement is driven by intraband currents from renormalized quasiparticles with frequency-dependent scattering rates.
   • In the PM insulating phase, the reduction in THG intensity upon cooling is dominated by the opening of the Mott gap, which suppresses the charge carrier density. This effect outweighs the orbital-charge coupling effects in this specific regime.

Significance and Claims
The paper claims to provide the first experimental demonstration of THz HHG in Mott insulators and to successfully model the complex temperature dependencies across the IMT. The authors assert that:

• THz HHG is feasible in Mott insulators even when the photon energy is far below the Mott gap, and unlike optical HHG, the enhancement in the AFM phase occurs for all harmonic orders, not just those exceeding the gap energy.
• The THz HHG response is highly sensitive to low-energy many-body interactions (spin-charge and orbital-charge couplings), offering a new spectroscopic tool to probe fundamental processes in complex correlated systems.
• The study validates the extension of nonequilibrium DMFT schemes to the THz range for modeling nonlinear light-matter interactions.
• These findings suggest strategies for efficient THz harmonic generation in strongly correlated systems, potentially expanding the class of materials for HHG applications beyond Dirac and topological materials.

The authors maintain a modest stance, noting that while the results offer insights into fundamental physics and potential strategies for efficiency, they do not propose specific immediate technological applications beyond the general scope of THz science and technology.