[Paper Review] Observation of Multiple Topological Corner States in Thermal Diffusion

Minghong Qi, Yanxiang Wang+5 more|arXiv (Cornell University)|Apr 25, 2023

Topological Materials and Phenomena4 citations

TL;DR

This study experimentally demonstrates multiple topological corner states in a 2D thermal diffusion system using a kagome lattice of thermal metamaterials. By exploiting the anti-Hermitian nature of the diffusion Hamiltonian, which yields purely imaginary eigenvalues corresponding to decay rates, the authors directly observe high-decay-rate corner states via temperature decay measurements, marking the first realization of such states in a pure diffusion system.

ABSTRACT

Higher-dimensional topological meta-materials have more flexible than one-dimensional topological materials, which are more convenient to apply and solve practical problems. However, in diffusion systems, higher-dimensional topological states have not been well studied. In this work, we experimentally realized the 2D topological structure based on a kagome lattice of thermal metamaterial. Due to the anti-Hermitian properties of the diffusion Hamiltonian, it has purely imaginary eigenvalues corresponding to the decay rate. By theoretical analysis and directly observing the decay rate of temperature through experiments, we present the various corner states in 2D topological diffusive system. Our work constitutes the first realization of multiple corner states with high decay rates in a pure diffusion system, which provides a new idea for the design of topological protected thermal metamaterial in the future.

Motivation & Objective

• To explore higher-dimensional topological states in diffusion systems, which remain underexplored despite their potential for practical applications.
• To realize a 2D topological structure in a thermal diffusive system using a kagome lattice of thermal metamaterials.
• To demonstrate the existence of multiple topological corner states with high decay rates in a pure diffusion environment.
• To provide a new design paradigm for topologically protected thermal metamaterials through experimentally accessible thermal systems.

Proposed method

• Design and fabricate a 2D kagome lattice thermal metamaterial to realize a topological system with anti-Hermitian diffusion Hamiltonian.
• Leverage the anti-Hermitian property of the diffusion Hamiltonian to ensure purely imaginary eigenvalues, corresponding to temperature decay rates.
• Perform direct experimental measurement of temperature decay dynamics to extract eigenvalues and identify corner states.
• Use theoretical modeling to confirm the topological nature and robustness of the observed corner states.
• Compare experimental decay rates with theoretical predictions to validate the presence of multiple corner states.

Experimental results

Research questions

• RQ1 Can multiple topological corner states be experimentally realized in a 2D thermal diffusion system?
• RQ2 How do the decay rates of corner states in a thermal diffusive system relate to the anti-Hermitian nature of the diffusion Hamiltonian?
• RQ3 What is the role of the kagome lattice structure in enabling multiple corner states in thermal diffusion?
• RQ4 Can topological protection be observed in a purely diffusive system without gain or loss mechanisms?

Key findings

• Multiple topological corner states with high decay rates were experimentally observed in a 2D thermal diffusion system based on a kagome lattice.
• The observed decay rates matched theoretical predictions derived from the anti-Hermitian diffusion Hamiltonian, confirming the presence of topologically protected states.
• The system exhibited purely imaginary eigenvalues, consistent with the non-Hermitian nature of the diffusion process.
• The corner states were robust and directly measurable through temperature decay dynamics, validating their topological origin.