🔬 mesoscale physics

Observation of Multiple Topological Corner States in Thermal Diffusion

This contribution presents the first experimental realization of multiple topological corner states with high decay rates in a two-dimensional thermal diffusion system based on a Kagome lattice and provides new insights for the development of topologically protected thermal metamaterials.

Original authors: Minghong Qi, Yanxiang Wang, Pei-Chao Cao, Xue-Feng Zhu, Fei Gao, Hongsheng Chen, Ying Li

Published 2026-05-06

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CC BY 4.0

Original authors: Minghong Qi, Yanxiang Wang, Pei-Chao Cao, Xue-Feng Zhu, Fei Gao, Hongsheng Chen, Ying Li

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 heat not as chaotic, spreading disorder, but as a traveler moving through a city governed by very specific rules. Normally, heat spreads when a hot spot is applied to a material, expanding evenly and slowly, like ink dropping into a glass of water. But in this paper, the researchers built a special "city" for heat where the rules are different, causing heat to get stuck at certain locations or vanish much faster than usual.

Here is the story of their discovery, broken down into simple concepts:

1. The City of Heat (The Kagome Lattice)

The researchers built a physical model from metal cylinders connected by thin rods and arranged in a honeycomb-like pattern known as a Kagome lattice. Imagine this as a playground with three swings (the cylinders) connected by ropes (the rods) in a triangular shape that repeats over and over.

They created two different versions of this playground:

Version A: The ropes connecting the swings within a triangle are short and thin, while the ropes leading to the next triangle are thick.
Version B: The ropes within the triangle are thick, and the ropes leading outward are thin.

They stitched these two versions together to form a large hexagon. The boundary where these two versions meet is where the magic happens.

2. The "Anti-Hermitian" Twist (Why Heat is Different)

In the world of light or sound (waves), energy usually remains constant as it moves. But in the world of heat (diffusion), energy constantly escapes. The paper notes that the mathematics describing this heat flow is "anti-Hermitian."

The Analogy: Imagine a ball rolling down a hill. In a normal world (waves), it could roll back and forth forever. In this world of heat, the hill is covered in thick mud. The ball doesn't just roll; it sinks in and slows down. The "speed" at which it sinks is what the researchers call the decay rate. A high decay rate means the heat disappears (cools) very quickly.

3. The Secret Corners (Topological Corner States)

Normally, when you mix two different materials, you might get a "road" (an edge state) along which heat travels along the boundary. But this team found something special: corner states.

The Analogy: Imagine a triangular park made of two different types of grass. If you throw a hot stone into the middle, it spreads everywhere. If you throw it at the edge, it spreads along the edge. But the researchers found that if you throw the hot stone exactly at the corner where the two grass types meet in a specific way, the heat gets "trapped" right at that point. It does not spread; it remains localized.

They found three different types of these trapped corners (labeled I, II, and III).

4. The Race to Cool Down (High Decay Rates)

The most exciting part of the experiment was timing how fast these trapped hot spots cooled down.

The Bulk State: Heat in the middle of the structure cooled slowly. It was like a heavy stone sinking in mud.
Corner State I: This cooled somewhat faster than the middle.
Corner States II and III: These were the superstars. They cooled much, much faster.

The Analogy: Imagine three buckets with holes in the bottom.

Bucket A (Bulk) has a tiny pinhole. Water trickles out slowly.
Bucket B (Corner I) has a small hole. Water trickles out faster.
Bucket C (Corner II/III) has a wide-open drain. The water (heat) disappears almost instantly.

The researchers proved that these specific "corner" positions act like super-drains for heat. They can dissipate thermal energy significantly faster than any other part of the structure.

5. How They Proved It

To test this, they 3D-printed a model of this lattice from metal. They used a heat gun to heat specific cylinders and frost spray to cool them, creating "hot spots." Then, they used a thermal imaging camera to observe how the heat disappeared over time.

The results matched their mathematics perfectly:

Heat at the special corners vanished quickly.
Heat in the middle stayed warm much longer.
The "trapped" heat did not spread to neighbors as much as expected, proving it was stuck at that specific corner location.

The Conclusion

The paper claims to be the first to show that you can create a structure where heat gets trapped in corners and disappears (cools) at a super-fast rate. They didn't just predict this with mathematics; they built it, heated it up, and filmed it cooling down.

This suggests that in the future, we could design materials that use these "super-drain" corners to manage heat efficiently, but the paper focuses strictly on the discovery of these states and their rapid cooling properties within this specific thermal system.

Technical Summary: Observation of Multiple Topological Corner States in Thermal Diffusion

Problem Statement
While topological concepts have revolutionized the physics of condensed matter and classical wave systems (photonic, acoustic, mechanical), their application to diffusion systems, particularly thermal metamaterials, remains largely unexplored. Previous research in thermal topological systems was largely restricted to one-dimensional setups or low-energy bands, limiting the discovery of unique topological states in higher dimensions. Furthermore, the potential of topological states with high decay rates in pure diffusion systems has not been uncovered, hindering the development of robust strategies for thermal regulation that leverage topological protection against defects and disorder.

Methodology
The authors experimentally realized a two-dimensional topological thermal metamaterial based on a Kagome lattice. The system consists of cylindrical sites connected by rods with varying cross-sectional areas ( $S_1$ and $S_2$ ) to control intracellular ( $D_1$ ) and intercellular ( $D_2$ ) thermal couplings.

Theoretical Framework: The evolution of the thermal field is governed by an anti-Hermitian Hamiltonian, leading to purely imaginary eigenvalues corresponding to thermal decay rates ( $\lambda = -\text{Im}(\omega)$ ). The bulk topology is characterized by a polarization derived from the Berry connection, distinguishing between "trivial" and "non-trivial" phases based on the coupling ratio $\Delta = D_1/D_2$ .
Design Strategy: To observe corner states, the researchers constructed a lattice in which a triangular region of non-trivial units ( $\Delta = 12.5$ ) is embedded in a background of trivial units ( $\Delta' = 1/\Delta$ ). This configuration creates interfaces between two distinct topological phases.
Simulation and Experiment: Finite-element simulations (COMSOL Multiphysics) were performed to predict temperature field distributions and decay rates. Experimentally, a stainless steel sample was fabricated using 3D metal printing. The surface was coated with black paint to minimize reflectivity for accurate infrared imaging. Initial temperature distributions were established using heat guns and freezing sprays to excite specific bulk and corner states. Temperature evolution was monitored with an infrared camera.

Main Contributions

Extension to Higher Dimensions: The work extends topological phases from one-dimensional thermal systems to a two-dimensional Kagome lattice, demonstrating that higher-dimensional topological states can exist in purely diffusive systems.
Discovery of Multiple Corner States: The study identifies and experimentally confirms the presence of multiple topological corner states (labeled I, II, and III) within the 2D thermal lattice.
High Decay Rate States: A key contribution is the revelation of topological states with "high decay rates." In contrast to traditional states confined within bandgaps, these states exist beyond standard energy bands and exhibit superior local heat dissipation speeds.
Experimental Realization: This represents the first experimental realization of multiple corner states with high decay rates in a pure diffusion system.

Results

Band Structure: Theoretical analysis revealed large bandgaps between the lower and middle energy bands, as well as a flat band at the upper edge of the middle band. The spectrum showed three edge states and three corner states.
Decay Rates: Simulations and experiments confirmed that the decay rates of the corner states correspond to the imaginary parts of the eigenvalues.
- Corner State III: Exhibited the fastest decay rate, with the maximum temperature dropping to 315.9 K after 20 seconds.
- Corner State II: Showed a significantly faster decay rate than the bulk state and Corner State I, reaching 319.3 K after 20 seconds.
- Corner State I: Displayed a decay rate greater than that of the bulk state but slower than that of II and III.
Localization: Thermography confirmed that the corner states, particularly II and III, maintained highly confined temperature fields with minimal heat spread to neighboring sites. The experimental decay curves agreed with theoretical predictions, validating the anti-Hermitian nature of the thermal diffusion Hamiltonian.

Significance
The work asserts that this study provides a new paradigm for the design of topologically protected thermal metamaterials. By demonstrating that multiple corner states with high decay rates can exist in a pure diffusion system, the authors offer a new mechanism for efficient heat dissipation and thermal management. The robustness of these topological states against defects suggests potential applications in thermal management, energy harvesting, and the design of novel thermal devices with unprecedented functionality. These findings bridge the gap between topological physics and thermal engineering, opening pathways for exploring higher-dimensional topological phenomena in diffusive systems.