Strong long-wavelength electron-phonon coupling in Ta$_2$Ni(Se,S)$_5$

This study identifies Ta$_2$Ni(Se,S)$_5$ as a rare "ultra-strong coupling" material by experimentally demonstrating that its quasi-one-dimensional excitonic insulator candidate exhibits extremely anisotropic phonon broadening and softening in the semimetallic normal state, driven by strong interband electron-phonon coupling with a dimensionless coupling constant of approximately 10.

The Gist

Imagine a dance floor where electrons (the negative dancers) and holes (the positive dancers) are supposed to pair up spontaneously to form a special, unified crowd called an "excitonic insulator." For years, scientists have been hunting for a real-world material where this happens naturally, but it's been like trying to find a specific dancer in a crowded room while the music is so loud (caused by the vibrating atoms of the material) that it's hard to hear the music they're dancing to.

This paper investigates a material called Ta₂NiSe₅ (and its cousin, Ta₂NiS₅) to see if it's the perfect dance floor for this phenomenon or if the "music" of the vibrating atoms is actually driving the show.

Here is the story of what they found, explained simply:

1. The Mystery: Who is Leading the Dance?

Scientists have two main theories about what happens in Ta₂NiSe₅:

• Theory A (The Exciton): The electrons and holes fall in love and pair up on their own, creating a new state of matter.
• Theory B (The Vibration): The atoms in the crystal lattice vibrate so strongly that they force the electrons and holes to rearrange, creating a similar-looking state but for a different reason.

It's like trying to tell if a crowd is moving because they are all following a single leader (the exciton) or because the floor itself is shaking so violently that everyone is jostled into a new formation (the vibrations).

2. The Experiment: Listening to the Atoms

To solve this, the researchers used a super-powerful X-ray camera (called Inelastic X-ray Scattering) to take a "movie" of how the atoms vibrate. They looked at two specific things:

• How fast the vibrations die out (Lifespan): If a vibration stops quickly, it means it's interacting strongly with something else.
• How the vibrations change speed (Softening): If a vibration slows down, it usually means the material is getting ready to change its shape.

They tested two materials:

1. Ta₂NiSe₅: A material that acts like a semi-metal (easy for electricity to flow) at high temperatures and changes into an insulator (blocks electricity) when cooled.
2. Ta₂NiS₅: A nearly identical material, but with sulfur instead of selenium. This one acts like a normal insulator (blocks electricity) all the time.

3. The Big Discovery: The "Ultra-Strong" Connection

The results were surprising and very specific:

• The "Hot" State: In the warm, semi-metallic version of Ta₂NiSe₅, the vibrations of the atoms were extremely short-lived and blurry. It was as if the atoms were vibrating frantically and crashing into the flowing electrons constantly.
• The "Cold" State: When Ta₂NiSe₅ cooled down and changed its structure, those frantic vibrations suddenly became calm and long-lasting.
• The Cousin (Ta₂NiS₅): In the sulfur version, the vibrations were calm and long-lasting in both hot and cold states.

The Analogy: Imagine a crowded hallway.

• In the warm Ta₂NiSe₅, the hallway is full of people running back and forth (electrons). If you try to wave your arms (vibrate an atom), you get bumped constantly, and your wave dies out instantly.
• In the cold Ta₂NiSe₅, the people have stopped running and are standing still in a grid. Now, when you wave your arms, no one bumps you, and your wave lasts a long time.
• In Ta₂NiS₅, the people are standing still in a grid no matter the temperature, so your wave is always calm.

4. What This Means

The researchers concluded that the "frantic" behavior in the warm Ta₂NiSe₅ is caused by a massive, direct connection between the moving electrons and the vibrating atoms.

They calculated that this connection is so strong it falls into a category they call "ultra-strong coupling."

• The Metaphor: Usually, electrons and atoms talk to each other politely. In this material, they are shouting at each other. The strength of this shout is about 10 times stronger than what is typically seen in other materials.

5. The Verdict on the "Excitonic Insulator"

Does this mean Ta₂NiSe₅ is not an excitonic insulator? Not necessarily, but it changes the story.

• If it were a pure "exciton" dance, the most chaotic vibrations should have happened when the material was cold and the excitons were formed.
• Instead, the chaos happened when the material was hot and the electrons were flowing freely.

This suggests that the transition in Ta₂NiSe₅ is driven primarily by the strong interaction between electrons and the vibrating lattice, rather than just electrons falling in love on their own. The "dance" is being led by the shaking floor, not just the partners.

Summary

The paper reveals that Ta₂NiSe₅ is a rare material where the connection between electricity and atomic vibration is incredibly powerful ("ultra-strong"). This strong connection is what causes the material to change its properties, rather than a simple pairing of electrons and holes. This discovery helps scientists distinguish between different types of exotic quantum states by simply "listening" to how the atoms vibrate.

Technical Summary

Technical Summary: Strong Long-Wavelength Electron-Phonon Coupling in Ta2Ni(Se,S)5

Problem and Context
The identification of intrinsic excitonic insulators (EI) in bulk materials has been historically complicated by the coexistence of strong electron-phonon coupling (EPC). While artificial quantum Hall bilayer systems allow for independent control of electron and hole populations to isolate excitonic effects, bulk materials present a challenge: interband EPC can generate electron-hole excitations and structural instabilities that mimic the charge redistribution of a bona fide excitonic insulator. The central problem addressed in this work is distinguishing whether the symmetry-breaking phase transition in the quasi-one-dimensional candidate Ta2NiSe5 is driven by exciton condensation (involving EI-phasons) or by strong interband electron-phonon coupling. Previous studies have yielded conflicting interpretations, with some suggesting excitonic condensation and others pointing to structural instabilities driven by lattice fluctuations.

Methodology
To resolve this ambiguity, the authors employ inelastic X-ray scattering (IXS) to map the low-energy phonon dynamic structure factor in momentum space. The study focuses on the Ta2Ni(Se,S)5 family, which offers a tunable system where increasing Sulfur (S) content drives the normal state from a semimetal (Ta2NiSe5) to a fully gapped semiconductor (Ta2NiS5), while suppressing the phase transition temperature ($T_S$).

The experimental approach involves:

1. IXS Measurements: Scanning along specific momentum trajectories, $(2.03 \ 0 \ 6+l)$ and $(2+h \ 0 \ 6)$, to probe transverse acoustic (TA), longitudinal acoustic (LA), and optical ($B_{2g}$) phonon modes in both Ta2NiSe5 and Ta2NiS5 across various temperatures.
2. Spectral Analysis: Extracting phonon linewidths (inverse lifetimes) and energies from energy-loss spectra, deconvolving the instrument resolution (1.5 meV).
3. Theoretical Comparison: Utilizing density functional theory (DFT) to calculate phonon-coordinate-dependent free energy potentials and anharmonic components.
4. Quantitative Estimation: Combining experimental phonon linewidths with ARPES-derived band structures to calculate the dimensionless electron-phonon coupling vertex ($g/\omega_0$) within the linear response framework.

Key Results
The study reveals a stark contrast in phonon behavior between the semimetallic normal state of Ta2NiSe5 and the broken-symmetry state of Ta2NiSe5 or the isostructural Ta2NiS5:

• Anisotropic Phonon Broadening: In the normal state of Ta2NiSe5, the 2 THz $B_{2g}$ optical phonon and the TA mode exhibit extremely anisotropic broadening. Specifically, the linewidth of the 2 THz mode increases substantially as momentum $q \to 0$ along the $c^*$ direction (L), while remaining resolution-limited along the $a^*$ direction (H).
• Absence in Gapped States: This dramatic broadening is completely absent in the broken-symmetry state of Ta2NiSe5 (below $T_S$) and in the fully gapped normal state of Ta2NiS5. In these gapped states, the phonons are long-lived.
• Softening vs. Broadening: While previous reports noted phonon softening at specific wavevectors, this study finds no dramatic softening of the 2 THz $B_{2g}$ mode across the phase transition in Ta2NiSe5. Instead, the primary anomaly is the lifetime reduction (linewidth increase) in the normal state.
• Coupling Strength: By analyzing the linewidths, the authors determine the dimensionless coupling ratio $g/\omega_0 \sim 10$. This places the Ta2Ni(Se,S)5 family in an "ultra-strong" coupling regime.
• Exclusion of Alternative Mechanisms:
  • Phason-Phonon Coupling: If the transition were driven by an EI-phason, significant broadening would be expected in the broken-symmetry state due to anticrossing with the phason. The observed broadening occurs only in the normal state, ruling this out as the primary driver.
  • Exciton Continuum: Strongest excitonic fluctuations are expected in the BEC limit (Ta2NiS5 normal state), yet no broadening is observed there.
  • Static Disorder: Diffuse scattering analysis confirms that the observed signals are dynamic (phononic) rather than static (impurities/dislocations).

Significance and Claims
The paper claims that the phase transition in the Ta2Ni(Se,S)5 family is closely related to strong interband electron-phonon coupling rather than exciton condensation or EI-phason dynamics. The experimental evidence suggests that the semimetallic normal state of Ta2NiSe5 provides a large density of low-energy electronic states that facilitate strong scattering, leading to the observed phonon broadening. Upon the opening of the $\sim 300$ meV band gap in the broken-symmetry state (or in Ta2NiS5), these low-energy excitations are suppressed, restoring long phonon lifetimes.

The authors conclude that Ta2Ni(Se,S)5 serves as a rare "ultra-strong coupling" material. They posit that high-resolution phonon spectroscopy acts as a general discriminator for intertwined phases, capable of distinguishing between excitonic and electron-phonon driven mechanisms based on the distinct signatures of phonon-elementary excitation coupling. The work establishes a direct experimental estimate of the EPC vertex, confirming the material's potential as a platform for investigating beyond-Born-Oppenheimer approximation behaviors, such as squeezed phonon states.