Loss induced delocalization of topological boundary modes.

The introduction of non-Hermiticity has inspired abundant intriguing phenomena to topological physics. As a significant part of non-Hermiticity, losses are generally inevitable, represent a natural tendency of open systems, and can be readily regulated by straightforward passive components. However, losses are originally considered obstructive to topological systems and usually enable the localization of states. Here, we present that reciprocal loss can induce delocalization of topological boundary modes, which is essentially distinct from non-reciprocal mechanisms. By precisely regulated imaginary hopping via loss, the end modes in one dimension and the corner modes in two and three dimensions of topological insulators are delocalized to the bulk, accompanied by the non-Hermitian skin effects. Our theory is implemented in passive electric circuits with resistance as non-Hermitian loss, and the topological delocalized modes are well visualized experimentally. The realized topological delocalized modes are still robust against disorders and possess a broadband property. Our work establishes an important missing link between topology and loss, and brings a unique vision for compact topological applications.