🔬 materials science

Non-equilibrium Effects in Vibrational Modes Pumped by Inelastic Tunneling

Using inelastic electron tunneling microscopy on the hydrogen-adsorbed Pd-terminated surface of the strongly correlated oxide PdCrO2, researchers demonstrated that localized vibrational modes exhibit unusually long lifetimes and distinct non-equilibrium signatures, a phenomenon attributed to the unique properties of the substrate.

Original authors: Chi Ming Yim, Owain T. Beynon, Seunghyun Khim, Chiara Gattinoni, Peter Wahl

Published 2026-07-21

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Chi Ming Yim, Owain T. Beynon, Seunghyun Khim, Chiara Gattinoni, Peter Wahl

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of atoms as a giant, bustling dance floor. In this microscopic party, the "dancers" are electrons, and the "floor" is made of atoms arranged in a crystal lattice. Sometimes, the floor itself wiggles and jiggles; these vibrations are called phonons. Usually, when you try to make a specific dancer jump or wiggle, the energy they gain is quickly stolen by the crowd around them, and the dance stops almost instantly. Scientists have long wondered if they could get these dancers to keep wiggling for a long time, creating a state of "non-equilibrium" where the energy doesn't just vanish. Why does this matter? Because if we can control these vibrations, we might be able to tune the properties of materials—like making them superconductors or better catalysts—simply by shaking them in just the right way. It's like trying to keep a swing moving by pushing it at the perfect moment, rather than letting it slow down and stop.

Now, let's zoom in on a very specific, high-tech dance floor made of a material called PdCrO₂. This isn't just any floor; it's a "strongly correlated" material, meaning the electrons on it are super sensitive to how the atoms move. The researchers in this study decided to play a game of "pin the tail on the donkey," but with hydrogen atoms. They stuck tiny hydrogen clusters onto the surface of this material, which formed a weird, non-repeating pattern of shapes (like a mosaic made of different-sized hexagons). Using a super-powerful microscope called a Scanning Tunneling Microscope (STM), they didn't just look at the hydrogen; they fired electrons at it to make the hydrogen vibrate.

Here is the big surprise: when they hit these hydrogen clusters with electrons, the vibrations didn't die out quickly like they usually do on metal surfaces. Instead, they kept wiggling for hundreds of picoseconds (that's a trillionth of a second, which is an eternity in the atomic world). The paper suggests that these vibrations are "non-equilibrium" because the researchers could actually see the hydrogen atoms getting "tired" of the constant pushing. When they pushed too hard (by increasing the electron current), the ground state of the vibration got "depopulated," meaning the atoms were stuck in the excited state for so long that they couldn't absorb new energy as fast as usual. This is a bit like trying to push a child on a swing who is already swinging so high and for so long that your next push just makes them wobble instead of go higher.

The team used a clever trick to figure out how long these vibrations lasted. They watched how the strength of the vibration signal changed as they increased the number of electrons hitting the surface. By comparing their real-world data to a simple "two-level" model (imagine a light switch that is either ON or OFF), they estimated that the vibrations in some of these clusters lasted between 11.3 and 519 picoseconds. That is significantly longer than what is seen on typical metal surfaces, where vibrations usually die out in less than a picosecond.

Why did this happen? The paper suggests it's because of the unique "personality" of the PdCrO₂ material. The surface layer of this material is somewhat disconnected from the bulk material underneath, acting like a shield that stops the energy from leaking away. Furthermore, the electrons in this material are "correlated," which means they don't screen out the vibrations as well as they do in normal metals. This lack of screening lets the vibrations hang around longer. The researchers also noticed that the most perfectly shaped clusters (the T1 and T7 types) had the longest-lasting vibrations, likely because their perfect geometry trapped the energy even better.

In short, this paper shows that by sticking hydrogen onto a very specific, exotic crystal, we can create vibrations that last much longer than expected. The authors suggest this is due to the special electronic and structural properties of the crystal, which protect the vibrations from dying out. While they didn't solve the mystery of every single vibration, their measurements and computer simulations strongly point to this "shielding" effect as the reason. This discovery is exciting because it hints that we might be able to use these long-lived vibrations to control how materials behave, potentially leading to better ways to make hydrogen fuel or new types of electronic devices.

Technical Summary: Non-equilibrium Effects in Vibrational Modes Pumped by Inelastic Tunneling

Problem Statement
Strongly correlated electron materials exhibit high sensitivity to lattice distortions, offering a pathway for tuning electronic ground states via selective vibrational driving. While optical excitations are commonly used for this purpose, atomistic-level studies of driving localized vibrational modes in quantum materials remain scarce. The specific challenge addressed in this work is the characterization of non-equilibrium vibrational excitation dynamics on the surface of a strongly correlated electron material using Scanning Tunneling Microscopy (STM) and Inelastic Electron Tunneling Spectroscopy (IETS). The authors investigate whether vibrational modes on such surfaces can be driven out of equilibrium and how their lifetimes compare to those on typical metal surfaces.

Methodology
The study focuses on the Pd-terminated surface of the delafossite oxide $\text{PdCrO}_2$ with chemisorbed hydrogen. Upon hydrogen adsorption, this surface forms a non-periodic tiling structure composed of tightly packed hydrogen clusters of varying sizes and shapes. The researchers employed STM-IETS to map inelastic processes with atomic resolution.

Spectroscopy: Differential conductance ( $g(V)$ ) and its derivative ( $g'(V)$ ) spectra were recorded to identify inelastic features corresponding to vibrational modes. Symmetry analysis ( $g'(V)$ vs. $-g'(-V)$ ) was used to confirm inelastic contributions.
Spatial Mapping: Spectroscopic imaging ( $g'(r, V)$ ) was performed over a $8 \text{ nm} \times 8 \text{ nm}$ region containing $\sim 50$ clusters to map the spatial distribution of excitation energies and intensities.
Non-equilibrium Analysis: To probe non-equilibrium effects, the intensity of vibrational modes was analyzed as a function of tunneling current ( $I_s$ ). At high currents, ground state depopulation is expected if the vibrational lifetime is sufficiently long.
Modeling: The experimental current-dependence data was fitted using a two-level excitation model (ground state and first excited state) to extract the spontaneous relaxation lifetime ( $\tau$ ) and the ratio of stimulated de-excitation to excitation rates ( $\kappa$ ). An extended $n$ -level model was also tested to verify robustness.
Theory: First-principles calculations were performed to compute vibrational lifetimes for hydrogen on the $\text{PdCrO}_2$ surface and compared with hydrogen on a $\text{Pd}(111)$ single crystal surface, accounting for antiferromagnetic ordering in the $\text{CrO}_2$ layer.

Key Results

Identification of Modes: Six distinct inelastic features were identified in the hydrogen clusters: $\alpha$ (3 meV), $\beta$ (15 meV), $\gamma_1$ (42 meV), $\gamma_2$ (84 meV), $\delta$ (59 meV), and $\epsilon$ (274 meV). The $\gamma_1$ mode corresponds to in-plane H-Pd bond vibrations, while $\epsilon$ corresponds to out-of-plane stretching. $\gamma_2$ is identified as the second harmonic (overtone) of $\gamma_1$ .
Spatial Localization: The $\gamma_1$ mode intensity is strongest at the center of the hydrogen clusters and decays toward the boundaries, confirming the localized nature of the vibrations.
High Quantum Yield: The excitation of the $\gamma_1$ mode exhibits a high quantum yield ( $\phi \approx 0.5$ ), attributed to the two-dimensional Fermi surface of the Pd layer which lacks states near the $\Gamma$ point, enhancing the cross-section for phonon-assisted tunneling.
Extended Lifetimes and Non-equilibrium Effects:
- The energy width of the $\gamma_1$ mode is limited by thermal broadening rather than intrinsic lifetime, suggesting a long-lived state.
- Analysis of the current dependence reveals a monotonic decrease in the normalized peak height ( $h_{norm}$ ) as tunneling current increases, indicating ground state depopulation.
- Fitting the data to the two-level model yields estimated lifetimes ( $\phi\tau$ ) ranging from 11.3 ps to 519 ps depending on the cluster type. Clusters T1 and T7, which possess perfect geometries, exhibit lifetimes an order of magnitude longer than other types.
- These lifetimes are significantly longer than those of adsorbates on typical metal surfaces (sub-picosecond to few picoseconds) but shorter than those on semiconducting/insulating surfaces (nanoseconds).
Theoretical Insights: Calculations confirm that the bending modes of hydrogen on the $\text{PdCrO}_2$ surface have lifetimes up to nine times longer than on $\text{Pd}(111)$ . The inclusion of antiferromagnetic ordering in the $\text{CrO}_2$ layer further increases these lifetimes, suggesting that electronic correlations reduce electronic screening, thereby inhibiting dissipation.

Significance and Claims
The paper demonstrates that vibrational excitations in hydrogen clusters on the $\text{PdCrO}_2$ surface can be driven into a non-equilibrium state with exceptionally long lifetimes compared to standard metal surfaces. The authors attribute this phenomenon to:

The unique structural and electronic anisotropies of the delafossite oxide.
Weak coupling between the surface Pd layer and the bulk material, which hampers electronic de-excitation along the stacking direction.
Reduced charge carrier density in $\text{CrO}_2$ compared to typical metals.
Electronic correlation effects that reduce electronic screening of the vibrational process.

The findings provide a mechanism for understanding the exceptional electrocatalytic activity observed during the hydrogen evolution reaction on the Pd surface of $\text{PdCoO}_2$ , suggesting that the extended vibrational lifetimes and inefficient dissipation play a role in this enhanced performance. The study establishes STM-IETS as a viable tool for probing non-equilibrium dynamics in strongly correlated systems and highlights the potential for tuning electronic states via selective vibrational driving in such materials.

Technical Summary: Non-equilibrium Effects in Vibrational Modes Pumped by Inelastic Tunneling

More like this