Quadrupole Topological Insulator in Non-Hermitian Thermal Diffusion

TL;DR

This paper demonstrates the creation of quadrupole topological phases in non-Hermitian thermal diffusion systems, revealing hierarchical boundary states and corner modes, thus expanding topological physics into diffusive regimes.

Contribution

It introduces a method to realize quantized bulk quadrupole moments in thermal diffusion, a feat not achieved in prior topological thermal metamaterials.

Findings

Observation of quadrupole topological phases in thermal systems

Hierarchical boundary states including corner modes

Both real and imaginary bands exhibit topological features

Abstract

Quantized bulk quadrupole moment has unveiled a nontrivial boundary state, exhibiting lower-dimensional topological edge states and simultaneously hosting the in-gap corner modes of zero dimension. All state-of-the-art strategies for topological thermal metamaterials have so far failed to observe such higher-order hierarchical features, since the absence of quantized bulk quadrupole moments in thermal diffusion fundamentally forbids the possible expansions of band topology, unlike its photonic counterpart. Here, we report a recipe of creating quantized bulk quadrupole moments in diffusion, and observe the quadrupole topological phases in non-Hermitian thermal systems. The experiments demonstrate that both the real- and imaginary-valued bands showcase the hierarchical hallmarks of bulk, gapped edge, and in-gap corner states, in stark contrast to the higher-order states only observed on real-valued bands in classic wave fields. Our findings open up unique possibilities for diffusive manipulations and establish an unexplored playground for multipolar topological physics.