Glass-like anomalies and unconventional thermoelectric transport in chimney ladder crystals

This study reveals that Nowotny chimney ladder crystals, specifically Ru$_2$Sn$_3$, exhibit glass-like thermodynamic and thermoelectric anomalies driven by low-energy optical phonons from their unique sublattice structure that hybridize with acoustic modes, leading to unconventional transport behaviors explained by a model of electron scattering with overdamped phonons.

The Gist

Imagine a world where materials are usually sorted into two strict camps: perfect crystals (like a neatly organized army marching in step) and amorphous glasses (like a chaotic crowd of people milling about randomly).

For a long time, scientists believed that if you wanted a material to act like glass—specifically, to be a terrible conductor of heat—you needed a messy, disordered structure. However, this paper introduces a new character to the story: the Nowotny Chimney Ladder (NCL) crystal. Think of these crystals as a unique architectural marvel where two different "ladders" (sublattices) are woven together. They look perfectly ordered from the outside, like a crystal, but they behave strangely, acting more like glass in some ways.

The researchers focused on a specific material called Ru2Sn3 (Ruthenium-Tin) to see what was going on. Here is what they found, explained simply:

1. The "Ghost" in the Machine (Glassy Heat Capacity)

When you heat up a normal crystal, its ability to store heat (heat capacity) follows a predictable, smooth curve. But when the researchers heated up Ru2Sn3, they found a weird "bump" or "hump" in the data at very low temperatures (around 8 to 14 Kelvin).

• The Analogy: Imagine a choir singing a perfect note. Suddenly, a few singers start humming a strange, low-frequency tune that wasn't in the sheet music. This extra "hum" is what the researchers call a boson peak. Usually, you only hear this kind of extra noise in disordered glasses, not in perfect crystals.
• The Cause: Using computer simulations, they discovered that inside this crystal, there are specific atoms (Tin) that are loosely held. They wiggle back and forth in a "corkscrew" motion or a "tilting" motion. These are low-energy optical phonons (vibrations). Because they are so easy to wiggle, they act like a crowd of people shuffling their feet, creating that "glassy" bump in the heat data.

2. The Traffic Jam (Thermal Conductivity)

In a perfect crystal, heat travels like a high-speed train on a straight track. In glass, heat moves like a car stuck in heavy traffic, constantly stopping and starting.

• The Finding: Ru2Sn3 conducts heat very poorly, similar to glass, even though it is a crystal.
• The Mechanism: The "corkscrew" vibrations mentioned above act like roadblocks. They crash into the main heat-carrying waves (acoustic phonons). Instead of passing each other smoothly, they get tangled up and "avoid" each other (a phenomenon called avoided crossing). This creates a traffic jam that slows down the flow of heat significantly.

3. The Strange Electrical Behavior

Because Ru2Sn3 is a metal, electricity flows through it. Usually, in metals, electrical resistance changes in a predictable way as you cool it down (often following a $T^5$ rule).

• The Anomaly: In Ru2Sn3, the electrical resistance behaves strangely. It follows a $T^2$ rule (a different mathematical pattern) and then stays perfectly linear for a long time as it gets colder.
• The Explanation: The researchers propose that the electrons (the carriers of electricity) are constantly getting "bumped" by those same wiggly, low-energy vibrations. It's like a runner trying to sprint through a field where the grass is constantly tripping them. These "overdamped" vibrations (vibrations that are sluggish and heavy) scatter the electrons in a way that creates this unusual resistance pattern.

4. The Big Picture

The most exciting part of this paper is that it proves you don't need disorder (messiness) to get "glassy" behavior.

• The Takeaway: You can have a perfectly ordered crystal structure, but if the internal "ladders" are arranged just right to create these specific, low-energy wiggles, the material will act like a glass.
• Why it matters: This gives scientists a new blueprint. Instead of trying to make messy, disordered materials to stop heat flow (which is hard to control), they can design ordered crystals with specific internal "wiggles" to achieve the same result. This could help in designing better materials for converting heat into electricity (thermoelectrics), where you want to stop heat from escaping but let electricity flow freely.

In summary: The paper shows that a crystal called Ru2Sn3 has a secret "dance floor" inside it where atoms wiggle in a way that mimics the chaos of glass. This internal dance slows down heat and messes with electricity in a way that was previously thought to only happen in messy, disordered materials.

Technical Summary

Technical Summary: Glass-like Anomalies and Unconventional Thermoelectric Transport in Chimney Ladder Crystals

Problem Statement
Theoretical descriptions of solid-state properties traditionally bifurcate into two paradigms: ideal ordered crystals, governed by Debye and Fermi liquid theories, and fully disordered amorphous solids, characterized by glassy anomalies such as the boson peak and low-temperature thermal conductivity plateaus. While certain complex crystals exhibit glass-like features, the microscopic origin of these anomalies in ordered systems remains debated. Specifically, it is unclear whether structural disorder is a necessary condition for glassy physics or if specific lattice dynamics in ordered crystals can induce similar behavior. Furthermore, the impact of such "glassy" modes on thermoelectric transport in metallic systems has not been systematically investigated, leaving a gap in understanding the interplay between glassiness and electronic transport in ordered intermetallics.

Methodology
The authors conducted an extensive experimental and theoretical investigation of the Nowotny chimney ladder (NCL) family of intermetallic crystals, with a primary focus on the compound $Ru_2Sn_3$.

• Experimental Characterization: High-quality single crystals ($Ru_2Sn_3$-#1 and #2) and polycrystalline Ga-doped samples were synthesized. Structural integrity was confirmed via single-crystal X-ray diffraction (XRD) and Rietveld refinement, verifying negligible structural disorder. Thermodynamic and transport properties were measured using a Physical Properties Measurement System (PPMS), including heat capacity ($C_p$), thermal conductivity ($\kappa$), electrical resistivity ($\rho$), Seebeck coefficient ($S$), and Nernst signal ($N$) over a wide temperature range.
• Theoretical Modeling: The study employed Density Functional Theory (DFT) at zero temperature and ab initio Molecular Dynamics (AIMD) simulations at finite temperature (100 K) to compute vibrational spectra, phonon dispersions, and anharmonic effects.
• Data Analysis: Experimental data were compared against Debye models and glassy scaling laws. Theoretical heat capacity was calculated via mode-resolved summation of the vibrational spectrum. A theoretical framework based on electron scattering with overdamped phononic modes was developed to explain resistivity anomalies, utilizing the Baym formula and spectral functions derived from the calculated phonon dispersions.

Key Results

1. Glass-like Heat Capacity: Despite being fully crystalline, $Ru_2Sn_3$ and related NCL materials exhibit a boson-peak-like anomaly in the heat capacity normalized by $T^3$ ($C/T^3$) within the 8–14 K range. This excess peak, which deviates from the Debye $T^3$ law, collapses onto a universal curve when normalized by peak position and intensity, mirroring behavior seen in amorphous solids like vitreous silica.
2. Microscopic Origin (Low-Energy Optical Modes): DFT and AIMD simulations reveal that this anomaly originates from extremely low-energy optical phonons (0.6 meV) arising from the unique chimney ladder sublattice structure. These modes correspond to "corkscrew-like" twisting of Sn helices and "canting" motions of Sn atoms. Crucially, these optical modes couple with acoustic phonons, causing avoided crossings and significant distortion of the acoustic dispersion. This hybridization leads to strongly modified acoustic modes that contribute to the heat capacity excess.
3. Anomalous Thermal Conductivity: The thermal conductivity of $Ru_2Sn_3$ is exceptionally low (comparable to glasses) and lacks the sharp peak typical of crystals. At low temperatures, $\kappa$ scales as $T^{3/2}$, deviating from the crystalline $T^3$ prediction and approaching the glassy $T^{2-\Delta}$ behavior. This regime correlates directly with the temperature range where the low-lying optical modes dominate the heat capacity.
4. Unconventional Electrical Resistivity: The electrical resistivity displays an extended linear-in-$T$ behavior and an anomalously large $T^2$ contribution at low temperatures, deviating from standard Fermi liquid ($T^2$) and electron-phonon ($T^5$) expectations. The crossover between these regimes occurs at temperatures comparable to the energy scales of the flat optical modes.
5. Thermoelectric Response: The Seebeck and Nernst signals exhibit anomalous plateaus in the 20–120 K range, strongly correlating with the energy scales of the low-lying optical phonons. The thermoelectric figure of merit ($ZT$) reaches a maximum of ~0.06 at 120 K.

Significance and Claims
The paper claims to demonstrate that glassy thermodynamic and transport behaviors can emerge in ordered crystals without the need for structural disorder or strong electronic correlations. The authors propose that the "chimney ladder" sublattice structure naturally generates extremely low-energy optical modes. The coupling of these modes to acoustic phonons creates avoided crossings and overdamped phononic behavior, which:

• Induces a boson-peak-like anomaly in heat capacity.
• Suppresses thermal conductivity via strong phonon scattering.
• Drives unconventional electrical resistivity (linear-in-$T$ and enhanced $T^2$) through electron scattering with overdamped phonons.

The work suggests that NCL crystals serve as a platform to explore the emergence of "strange metal" physics and glassy phenomena in ordered systems. It outlines a pathway for designing metallic materials with low thermal conductivity and unique thermoelectric properties by engineering specific sublattice arrangements to induce low-energy optical modes, rather than relying on disorder. The authors note that while the current $ZT$ is modest, the intrinsic low lattice thermal conductivity of the parent compound offers a foundation for future optimization via doping or microstructural engineering.