Researchers at ETH Zurich and collaborating institutions have demonstrated a way to surpass limitations on atomic motion within a class of materials called sliding ferroelectrics. The work reveals that conventional expectations of proportionality between force and displacement, Hooke’s law, break down under intense optical excitation, a phenomenon that typically limits how much a crystal lattice can be displaced.

Instead of increasing the power of light pulses, the team found that precisely timing multiple pulses allows for markedly larger phonon amplitudes at a fixed energy level. This approach exposes a regime of anharmonic phonon coupling, opening new pathways for steering lattice motion in quantum materials.

WTe₂ Sliding Ferroelectric Structure and Polarization Origin

Van der Waals material tungsten ditelluride (WTe₂) exhibits a surprising response to optical excitation; conventional expectations of increasing atomic motion with pulse strength fail as the material approaches a saturation point. Researchers discovered that the amplitude of a key phonon mode, important for controlling ferroelectric polarization, actually diminishes under single-pulse excitation. This behavior deviates from the established principle that lattice-driving forces scale linearly with photo-excited carrier density, a finding with implications for materials designed to manipulate polarization.

First-principles calculations attribute this nonlinear limitation to band-specific electron-phonon coupling, which generates competing forces on the lattice structure. The work reveals that populating certain electronic states counteracts the generation of the sliding phonon responsible for ferroelectric behavior. This is not a simple case of diminishing returns. The material actively resists further displacement beyond a certain threshold when driven by a single, powerful light pulse.

The frequency of the A₁ mode is 0.24 THz, while the B₁ mode registers at 2.7 THz, and the interlayer sliding mode directly couples to the out-of-plane ferroelectric polarization. However, the team bypassed this limitation by altering the timing of the optical drive, not the strength. This approach avoids simultaneously populating the counteracting electronic states, effectively “steering” the lattice motion beyond the saturation point observed with single-pulse excitation.

“Maximizing the sliding-mode amplitude provides greater leverage over the ferroelectric polarization,” the researchers note, highlighting the potential for enhanced control over the material’s properties. The resulting enhanced sliding motion exposes a regime of anharmonic phonon coupling that emerges only far from equilibrium. Time-resolved second-harmonic generation (trSHG) served as the primary method for probing these structural dynamics, owing to its sensitivity to inversion-symmetry breaking.

Fluence-dependent trSHG measurements revealed that increasing absorbed fluence from 0.4 to 6.5 mJ cm⁻² progressively shifts the equilibrium position towards the centrosymmetric Pnma configuration, leading to a softening of the sliding mode. The researchers emphasize that the 1T’ and Td phases of WTe₂ are not related by a group-subgroup relationship, a nuance important for understanding the material’s complex behavior.

The findings demonstrate a pathway to overcome limitations in lattice displacement, a critical challenge in controlling the polarization of sliding ferroelectrics. This precise control over phonon amplitudes unlocks access to nonlinear lattice phenomena previously inaccessible through conventional excitation methods, potentially enabling new devices and applications using the unique properties of these materials.

DECP Limitations in Sliding Ferroelectrics via Electron-Phonon Coupling

First-principles calculations reveal that the observed saturation in lattice displacement stems from band-specific electron-phonon coupling, creating competing forces that ultimately hinder the motion of atoms within the material. These calculations pinpoint how the driving force on the sliding mode changes with electronic temperature, demonstrating a shift in behaviour above and below an amplitude-limiting threshold. Specifically, the team found that the interlayer sliding phonon, responsible for the ferroelectric properties, not only saturates under strong light pulses but can actually diminish in amplitude, a counterintuitive result challenging conventional understanding of light-matter interaction.

This unexpected behaviour prompted a shift in experimental approach, moving away from simply increasing the power of the optical excitation. Instead, the researchers split the optical energy into two precisely timed pulses, designed to avoid simultaneously populating electronic states that induce these counteracting forces.

The resulting enhanced sliding motion then unlocks a regime of anharmonic phonon coupling, a state where the usual linear relationship between force and displacement breaks down and previously inaccessible lattice dynamics become possible. The ability to surpass these nonlinear limits has broad implications for controlling functionality in quantum materials, as large-amplitude coherent lattice motion provides a powerful route to manipulating their properties.

This is particularly relevant for van der Waals sliding ferroelectrics, where polarization is maintained even in extremely thin layers, and where driving this sliding motion to extreme amplitudes could enable ultrafast switching. “Understanding the fluence-dependent behaviour of the sliding-mode amplitude requires going beyond the conventional, linear DECP model, which assumes a linear relationship between excited-carrier density and coherent-phonon amplitude,” the study explains, highlighting the need for a more detailed approach to vibrational control.

The principles demonstrated with tungsten ditelluride (WTe₂) are expected to be broadly applicable to other similar materials and their vibrational degrees of freedom. This sequential excitation technique, therefore, provides a powerful means to investigate and tailor phonon-electron and phonon-phonon interactions far from equilibrium, potentially opening new avenues for materials design and control.

Time-Resolved Second-Harmonic Generation Measures Phonon Saturation

Time-resolved second-harmonic generation revealed a surprising saturation point in the interlayer sliding phonon governing ferroelectricity, with the amplitude initially increasing with excitation before declining above approximately 1.6 mJ cm⁻², a finding that challenges conventional expectations of lattice displacement. This counterintuitive reduction in coherent lattice motion imposes a fundamental limit on manipulating ferroelectric properties through light, a phenomenon observed in both tungsten ditelluride and molybdenum ditelluride.

Researchers discovered this saturation behavior is specific to the sliding mode, while higher-frequency modes continued to exhibit a monotonic increase in amplitude, suggesting a unique dynamic at play within these materials. Photo-excited electrons and holes near the Fermi level induce charge density modulation, driving nuclear displacements aligned with the sliding mode, but populating high-energy states creates a more homogeneous charge density that suppresses this motion.

This process effectively counteracts the initial driving force, limiting the achievable lattice displacement and demonstrating a breakdown of the linear relationship between excitation and atomic motion. The team’s simulations, solving equations describing the system, illustrate how a single driving pulse generates a coherent phonon amplitude, while two-pulse excitation can overcome the saturation limit. Splitting an optical pulse into two time-separated excitations proved to be a successful strategy for surpassing this amplitude saturation, enhancing control over ferroelectric polarization and enabling access to nonlinear lattice phenomena.

“In a real-space picture, the generation of photo-excited electrons and holes near $E_{F}$ induces a spatial modulation of the charge density within the unit cell,” the study explains, detailing how this transient distribution drives nuclear displacements. The simulations show that a time delay coinciding with one full phonon period results in resonant excitation, maximizing the effect. This technique offers a pathway to investigate and tailor phonon-electronic interactions, potentially unlocking new functionalities in quantum materials and beyond.

Two-Pulse Timing Surpasses Amplitude Limits in WTe₂

Measurements of the sliding ferroelectric material reveal that increasing the absorbed fluence from 0.5 mJ cm⁻² progressively softens the sliding mode, suppressing the signal and shifting the equilibrium position toward a centrosymmetric configuration. This softening, reflected in long-lived signal suppression and fluence-dependent frequency shifts, demonstrates a saturation point for conventional excitation methods. Researchers overcame this limitation by employing a double-pulse excitation strategy, enabling independent control of phonon amplitude within a targeted excited state.

This approach, detailed in recent work, demonstrates that redistributing the energy of a single ultrafast excitation into two precisely timed pulses surpasses the amplitude limitations of key vibrational modes. The team’s findings show that the assumption of a linear coupling between excited-carrier density and coherent vibrational amplitude, a principle used in displacive excitation of coherent phonons, is an oversimplification. This simplification can limit accessible lattice dynamics, but sequential excitation offers a pathway to avoid those limits.

Theoretical modeling, based on solving the coherent-phonon equation of motion, attributes this saturation to the material’s specific electronic structure. Analysis of time-resolved second-harmonic generation data further clarifies the mechanism. This suggests that the two-pulse technique not only increases amplitude but also reduces energy dissipation, allowing for more sustained and controlled lattice motion.

Anharmonic Phonon Coupling Emerges Beyond Equilibrium

Large-amplitude coherent lattice motion unlocks control over functionality in quantum materials, but conventional excitation methods encounter limitations. Femtosecond light pulses, typically used to initiate structural changes, can drive solids beyond equilibrium, yet achieving sustained and amplified motion proves challenging. Recent work demonstrates that surpassing these limits requires a shift in approach, focusing on the precise timing of optical stimuli rather than simply increasing their power.

The breakdown of linear relationships between driving force and lattice displacement marks a regime of anharmonic phonon coupling, observed only when systems are pushed far from equilibrium. Researchers found that a single pulse can induce saturation, hindering further increases in atomic motion, while a carefully orchestrated sequence avoids this compensation. This necessitates accounting for the contributions of individual electronic states to the effective electron-phonon coupling at the sliding-mode frequency.

The researchers explored WTe₂, a ferroelectric van der Waals semimetal, as a model system due to its giant magnetoresistance and ultrafast optical switching capabilities. This detailed analysis revealed coupling coefficients essential for capturing the transition pathways between phases. The study demonstrates that staggered sliding-mode stimulation restores linearity and amplifies sliding motion beyond the single-pulse limit. The ability to manipulate atomic motion with such precision promises advancements in areas ranging from data storage to energy harvesting.

Distinguishing Interlayer Sliding from True Shear Modes

The interlayer sliding motion observed in WTe₂ is often described as a shear mode in existing literature, but this categorization is inaccurate; the phenomenon does not alter the crystal’s elastic tensor, meaning it isn’t a true shear mode in the strict physical sense. This distinction is critical because it clarifies the fundamental mechanisms driving structural changes within the material and impacts how researchers interpret experimental results.

Understanding this difference allows for a more precise description of the pathways between different phases of the material, specifically the transition between the Td and 1T’ polymorphs. The lowest-energy route connecting the Td and 1T’ phases requires the simultaneous excitation of both interlayer sliding and intralayer shearing, bypassing an energetically unfavorable Pnma structure. This complex interplay is revealed through an anharmonic phonon expansion performed around the minimum energy structure, yielding a free energy function that details the relationship between vibrational spectrum and structural distortions.

The expansion, represented as F = $F_{T d}$ + $ω_{A_1}^{2} Q_{A_1}^{2}$ + $ω_{B_1}^{2} Q_{B_1}^{2}$ + γ $Q_{A_1} Q_{B_1}^{2}$ , demonstrates how the amplitude of the interlayer-sliding phonon, $Q_{A_1}$ and the intralayer-shear phonon, $Q_{B_1}$ , are coupled. This coupling is essential for accurately modeling the material’s behavior under external stimuli. Further analysis, extending the free energy expansion up to sixth order, identifies key coefficients, γ, η₁, and η₂, that capture the transition process between phases.

The manuscript’s findings were led by J.G.H., with overall guidance and support from M.F., and all authors contributed to the discussion and refinement of the results. The research also clarifies the relationship between the Pnma phase and the two relevant distortions, the interlayer sliding mode and the intralayer shear mode, which give rise to the Td and 1T’ phases respectively.

The $Γ_{2}^{–}$ distortion breaks inversion symmetry, leading to the ferroelectric Td phase, while the $Γ_{4}^{}$ + distortion results in monoclinic symmetry, corresponding to the 1T’ phase. This detailed understanding of the structural pathway and the associated vibrational modes provides a foundation for manipulating the material’s properties and exploring new functionalities. Data and code supporting the study’s findings are available upon reasonable request from the corresponding author, J.G.H.

Source: https://www.nature.com/articles/s41567-026-03491-1

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