Indian Scientists Discover Wave-Like Heat Flow in Crystals

In a breakthrough that challenges long-standing theories of heat transport in solids, researchers at the Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), an autonomous institute under the Department of Science and Technology (DST), have uncovered an unusual mechanism by which heat travels through a crystalline material — behaving more like a wave than a stream of particles.

Published in the prestigious journal Proceedings of the National Academy of Sciences (PNAS), USA, the study reveals a rare particle-to-wave crossover of phonons, fundamentally reshaping our understanding of thermal transport in solids with local structural disorder. The findings open new pathways for designing next-generation thermoelectric materials and advanced thermal management technologies.

Moving Beyond the Classical "Phonon Gas" Model

For decades, heat transport in solids has been explained using the "phonon gas" model, where phonons — quantized vibrations of atoms — behave like particles that scatter as they travel through a crystal lattice.

However, the JNCASR team, led by Prof. Kanishka Biswas of the New Chemistry Unit (NCU), has demonstrated that in a newly studied material — a zero-dimensional inorganic metal halide Tl₂AgI₃ — phonons can abandon particle-like motion and instead propagate through wave-like coherence, tunnelling between localized vibrational states.

This crossover from particle-dominated to wave-dominated heat transport is rarely observed experimentally and had largely remained a theoretical concept.

Record-Low Thermal Conductivity with Unusual Temperature Behaviour

The material exhibits an exceptionally low lattice thermal conductivity of ~0.18 W/m·K, placing it among the lowest known for crystalline solids.

More strikingly, instead of decreasing steadily with temperature — as predicted by conventional phonon scattering theory — the thermal conductivity becomes nearly temperature-independent above ~125 K, signalling a breakdown of the classical phonon gas picture.

Detailed analysis revealed that around 175 K, wave-like coherent transport overtakes particle-based scattering as the dominant mechanism of heat flow.

Crystal Chemistry Unlocks the Mechanism

At the heart of this discovery lies the unique crystal structure of Tl₂AgI₃. Unlike conventional three-dimensional frameworks, the material consists of discrete, cluster-like building blocks, introducing inherent local instability.

Drawing inspiration from Linus Pauling's third rule of crystal chemistry — which states that edge- or face-sharing coordination polyhedra increase cation–cation repulsion — the researchers hypothesized that strong repulsion between closely packed cations could destabilize the lattice locally.

Their experiments confirmed pronounced local distortions of silver atoms, producing extreme lattice anharmonicity — a condition where atomic vibrations deviate significantly from ideal harmonic motion.

This intense anharmonicity enhances phonon scattering to such an extent that conventional particle-like heat transport collapses. As the average phonon mean free path (lph) becomes shorter than the average atomic spacing (aav), heat begins propagating via wave-like tunnelling between localized vibrational states.

As Prof. Biswas explains:

"Tl₂AgI₃ is a rare example of a material that behaves simultaneously like a crystal and a glass. It retains long-range crystalline order, yet conducts heat in a glass-like manner due to phonon localization and wave-like coherence."

Advanced Experiments and Cutting-Edge Theory

The breakthrough was achieved through an integrated experimental and theoretical effort combining:

• Synchrotron X-ray pair distribution function analysis

• Low-temperature thermal transport measurements

• Raman spectroscopy

• Advanced first-principles calculations

A key innovation was the application of the linearized Wigner transport equation, recently developed by Prof. Swapan K. Pati's group at JNCASR. This framework allowed the team to rigorously distinguish between particle-like and wave-like heat transport contributions.

The experimental work was led by Dr. Riddhimoy Pathak, Ph.D. student in Prof. Biswas's group, while theoretical modelling was spearheaded by Mr. Sayan Paul from Prof. Pati's Theoretical Sciences Unit (TSU), serving as joint first author.

"This is a rare experimental realization of a concept that was largely theoretical," Prof. Biswas noted. "Crystalline solids do not have to be strictly particle-like in how they carry heat. They can access a mixed regime where wave-like coherence dominates, leading to ultralow and glassy thermal conductivity."

Implications for Thermoelectrics and Thermal Management

Ultralow thermal conductivity is a key requirement for high-performance thermoelectric materials, which convert waste heat into electricity. Materials that conduct electricity efficiently while blocking heat flow are central to sustainable energy technologies.

The discovery establishes a new design strategy:

• Leveraging chemical rules to induce local lattice instability

• Engineering phonon localization and coherence

• Creating crystalline materials with glass-like thermal transport properties

Such materials could be transformative for:

• Thermoelectric power generation

• Electronic device thermal management

• Energy-efficient cooling systems

• High-performance semiconductor platforms

Global Collaboration and National Infrastructure

The research utilized national supercomputing facilities and international synchrotron resources under the India@DESY programme, highlighting India's expanding research infrastructure and global scientific engagement.

A New Chapter in Materials Physics

By revealing how heat can transition from particle-like scattering to coherent wave transport within a crystalline solid, the study challenges textbook assumptions and opens a new frontier in solid-state physics.

This achievement underscores India's growing leadership in advanced materials research, demonstrating how deep chemical insight combined with state-of-the-art experimental and theoretical tools can uncover entirely new physical regimes with strong technological relevance.