Strong Optical-Optical Avoided Crossings Suppress Thermal Conductivity in Ga-Substituted TlInTe$_2$

This study demonstrates that substituting 50% of indium with gallium in TlInTe$_2$ induces symmetry-allowed optical-optical avoided crossings that significantly suppress phonon group velocities, thereby reducing the material's lattice thermal conductivity.

The Gist

Imagine a crystal lattice as a busy, three-dimensional highway system where heat travels in the form of tiny, vibrating particles called phonons. Usually, the "fast lanes" of this highway are the acoustic phonons (low-frequency vibrations), which zoom along quickly and carry most of the heat. The "slow lanes" are the optical phonons (high-frequency vibrations), which usually just shuffle around and contribute very little to the heat traffic.

In most materials, scientists try to slow down the fast lanes to stop heat from moving too easily. However, in a specific material called TlInTe₂, the researchers found something unusual: the slow lanes (optical phonons) were actually doing most of the heavy lifting, carrying about 63% of the heat!

The Problem: Crossing Paths

In the original TlInTe₂ crystal, these heat-carrying vibrations move along a specific path (the "c-axis"). As they travel, some of the slow lanes (optical phonons) try to cross paths with each other. Because these two lanes have different "symmetry" (think of them as cars driving on the left side of the road vs. the right side), they don't interact. They simply cross over each other like two trains passing on parallel tracks without ever touching. This allows them to keep their speed and carry heat efficiently.

The Solution: The "Traffic Jam" Trick

The researchers, Sayan Paul and Swapan K. Pati, decided to play a game of "musical chairs" with the atoms. They took the Indium (In) atoms in the crystal and swapped 50% of them with Gallium (Ga) atoms.

This small change did something magical to the symmetry of the crystal:

1. Before the swap: The crossing phonon lanes had different symmetries, so they ignored each other and crossed safely.
2. After the swap: The Ga atoms changed the rules so that the crossing lanes now had the same symmetry.

Now, imagine two cars trying to drive down the exact same lane at the same time. They can't pass through each other; they have to repel. In physics, this is called an avoided crossing. Instead of crossing, the two phonon branches push away from each other, creating a "gap" or a bump in the road.

The Result: Flattening the Road

This "repulsion" forces the phonon paths to flatten out, like a rollercoaster track that suddenly turns into a flat, bumpy road. When the road flattens, the phonons lose their speed (group velocity).

• The Outcome: Because the optical phonons slowed down so much, their ability to carry heat dropped significantly.
• The Numbers: The contribution of these optical phonons to heat transport fell from 63% down to 44%. Consequently, the total heat flow (thermal conductivity) of the material dropped from 0.568 to 0.482 (in standard units).

Why This Matters

Usually, scientists ignore the "slow lanes" (optical phonons) because they think they don't carry much heat. This paper proves that in certain materials, these slow lanes are actually the main highways. By using a chemical "switch" (swapping Indium for Gallium) to force these lanes to collide and repel, the researchers created a traffic jam that successfully slowed down the heat.

In short: They found a way to make the "slow" vibrations crash into each other, forcing them to slow down even more, which makes the material much better at blocking heat flow. This is a new trick for making materials that are excellent at insulating heat, which is useful for things like thermoelectric devices and thermal barrier coatings.

Technical Summary

Problem Statement
In crystalline solids, the suppression of lattice thermal conductivity ($\kappa_l$) is a critical objective for thermoelectric and thermal management applications. While the mechanism of avoided crossings between acoustic and optical phonons is well-established as a strategy to reduce $\kappa_l$ by scattering heat-carrying acoustic modes, the role of avoided crossings among optical phonons themselves has remained largely unexplored. This oversight stems from the general assumption that optical phonons contribute minimally to heat transport due to their low group velocities and short mean free paths. However, recent findings in materials like SnSe and BaSnS2 indicate that optical phonons can contribute significantly (up to ~68%) to total $\kappa_l$. Consequently, there is a need to investigate whether engineering optical phonon dispersion, specifically through optical–optical avoided crossings, can effectively modulate thermal transport in systems where optical modes are dominant.

Methodology
The authors employed first-principles density functional theory (DFT) calculations using the Vienna Ab initio Simulation Package (VASP) with the PBEsol functional and projected augmented wave (PAW) pseudopotentials. The study focused on the ternary chalcogenide TlInTe2 and its 50% Gallium-substituted variant, TlIn$_{0.5}$Ga$_{0.5}$Te$_2$.

• Harmonic Properties: Phonon dispersions and second-order interatomic force constants (IFCs) were calculated using the finite displacement method via the Phonopy package on a $3\times3\times3$ supercell.
• Anharmonic Properties: Third-order IFCs were derived using Phono3py from a $2\times2\times2$ supercell to account for phonon-phonon scattering.
• Thermal Transport: The lattice thermal conductivity ($\kappa_l$) was evaluated by solving the linearized Wigner transport equation (LWTE). This formalism separates $\kappa_l$ into a population term ($\kappa_p$, particle-like transport described by the Boltzmann transport equation) and a coherence term ($\kappa_c$, wave-like transport arising from quasi-degenerate mode coupling).
• Analysis: The study utilized irreducible representation analysis to determine the symmetry of phonon modes, cumulative $\kappa_l$ analysis to quantify mode contributions, and mode-averaged transport parameters (group velocity $v_g$, relaxation time $\tau$, and Grüneisen parameter $\gamma$) to identify the dominant suppression mechanisms.

Key Contributions and Results
The paper demonstrates that chemical substitution (50% Ga for In) in TlInTe2 induces a symmetry modification that transforms optical phonon crossings into avoided crossings, thereby suppressing thermal conductivity.

1. Optical-Dominated Transport in Pristine TlInTe2: Contrary to the typical acoustic-dominated model, pristine TlInTe2 exhibits strong optical phonon-dominated heat transport. At 300 K, optical phonons contribute approximately 63% to the total $\kappa_l$ (0.568 Wm$^{-1}$K$^{-1}$), driven by highly dispersive optical branches, particularly along the crystallographic $c$-axis ($\Gamma$–Z direction).
2. Symmetry-Induced Avoided Crossings: In pristine TlInTe2, several optical phonon branches cross in the dispersion relation. Irreducible representation analysis reveals these crossing branches belong to different symmetry representations (e.g., $A_{2u}$ vs. $B_{2g}$), rendering them non-interacting. Upon 50% Ga substitution, the crystal symmetry changes such that these previously crossing branches now possess the same symmetry representation. This allows the modes to hybridize and repel, creating characteristic avoided crossings with finite frequency gaps.
3. Suppression of Group Velocity and $\kappa_l$: The emergence of avoided crossings leads to a pronounced flattening of the optical phonon dispersion, significantly reducing the phonon group velocity ($v_g$) in the 100–125 cm$^{-1}$ and 150–200 cm$^{-1}$ frequency ranges. Consequently, the contribution of optical phonons to $\kappa_l$ drops from 63% to 44%, and the total $\kappa_l$ of TlIn$_{0.5}$Ga$_{0.5}$Te$_2$ is reduced to 0.482 Wm$^{-1}$K$^{-1}$ at 300 K.
4. Mechanism of Suppression: Mode-averaged analysis confirms that the reduction in $\kappa_l$ is primarily governed by the reduced group velocity ($\bar{v}_g$) induced by the avoided crossings. While the anharmonic scattering rate increases slightly (indicated by a higher average Grüneisen parameter $\bar{\gamma}$ and lower relaxation time $\bar{\tau}$), this provides only a secondary contribution to the thermal conductivity suppression.
5. Coherence vs. Population: The study finds that the population term ($\kappa_p$) dominates heat transport in both compounds, with the coherence term ($\kappa_c$) making a negligible contribution.

Significance
The authors establish that symmetry-modified optical–optical avoided crossings constitute an effective route to suppress lattice thermal conductivity in systems where optical phonons are the primary heat carriers. By demonstrating that chemical substitution can alter the symmetry characteristics of phonon modes to induce hybridization and gap opening, the work provides a distinct mechanism for engineering thermal transport. This approach offers a new pathway to reduce $\kappa_l$ beyond traditional strategies focused solely on acoustic phonon scattering, specifically targeting materials where optical modes significantly contribute to heat transport.