Year: 2025
Type: article
Abstract: Braiding is one of the oldest crafting techniques in human history, yet today it plays a key role across a wide range of scientific disciplines, from biology to physics. However, how fractal geometry interplays with non-Hermitian band braiding remains unexplored. Here, we bridge fractal physics and non-Hermitian topology by introducing topological fractal braiding, which can produce self-similar topological winding matrices. Furthermore, through tight-binding lattice model construction, we prove these fractal winding matrices govern non-Hermitian skin modes, yielding a scale-invariant skin effect where the ratio of left- to right-localized skin modes remains conserved through fractal iterations. We design and fabricate reconfigurable non-Hermitian topoelectrical circuits to experimentally reconstruct the fractal braiding of non-Hermitian bands, confirming our theory. Our work resolves how fractal geometry manifests in non-Hermitian band braiding and impacts skin effects, demonstrating scalable control of complex spectral topologies. While non-Hermitian physics and fractal geometry have been widely studied, their interplay in band braiding remains largely unexplored. The authors establish topological fractal braiding in non-Hermitian systems with scale-invariant skin effects, experimentally demonstrated using reconfigurable circuits.
Source: Communications Physics
Authors: Wenhui Cao, Xianru Qin, Weixuan Zhang, Xiaoqi Zhou, Xiangdong Zhang
Institution: Beijing Institute of Technology
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,990
Awards: G3114819178, G8469884905
OpenAlex ID: W4414627857