A research team led by Professors Chen Shuqi and Cheng Hua of Nankai University, in collaboration with Academician Liu Zhengyou and Professor Deng Weiyin of Wuhan University, has challenged the conventional understanding of loss in topological physics. By constructing a bilayer structure supporting pseudospin degrees of freedom and introducing only loss, the team successfully delocalized the topological boundary modes that were originally localized at ends or corners into the bulk lattice, realizing loss-induced topological delocalized modes. Their findings have been published in the internationally renowned journal Nature Communications under the title “Loss-induced Delocalization of Topological Boundary Modes”.

Figure: Schematic of loss-induced topological delocalized modes based on bilayer structure and pseudospin degrees of freedom

The researchers designed a bilayer structure with pseudospin degrees of freedom and utilized loss to achieve spin-polarized non-reciprocal pure imaginary coupling (see figure). By precisely tuning loss parameters, topological boundary modes within the bandgap can be delocalized into the bulk lattice, forming topological delocalized modes. This process occurs alongside the emergence of spin-dependent, more localized topological boundary modes. The topological delocalized modes remain topologically non-trivial and retain robustness against perturbations and disorders. Using passive circuits with resistors as the non-Hermitian loss across various dimensions, the team experimentally visualized these loss-induced topological delocalized modes. This study establishes a critical bridge between topological physics and non-Hermitian loss, providing new insights for developing compact and efficient non-Hermitian topological devices.

This work was completed under the primary affiliation of Nankai University. Tang Yugan, a doctoral student at Nankai University, and Wu Ji’en, a young faculty member at Changsha University of Science and Technology, are co-first authors. Corresponding authors include Professors Chen Shuqi and Cheng Hua of Nankai University, as well as Academician Liu Zhengyou and Professor Deng Weiyin of Wuhan University.

Link to the paper: https://doi.org/10.1038/s41467-025-65422-7

（Edited and translated by Nankai News Team.)