Topological modes (TMs) are usually localized at defects or boundaries of a much larger topological lattice^1,2. Recent studies of non-Hermitian band theories unveiled the non-Hermitian skin effect (NHSE), by which the bulk states collapse to the boundary as skin modes^3,4,5,6. Here we explore the NHSE to reshape the wavefunctions of TMs by delocalizing them from the boundary. At a critical non-Hermitian parameter, the in-gap TMs even become completely extended in the entire bulk lattice, forming an ‘extended mode outside of a continuum’. These extended modes are still protected by bulk-band topology, making them robust against local disorders. The morphing of TM wavefunction is experimentally realized in active mechanical lattices in both one-dimensional and two-dimensional topological lattices, as well as in a higher-order topological lattice. Furthermore, by the judicious engineering of the non-Hermiticity distribution, the TMs can deform into a diversity of shapes. Our findings not only broaden and deepen the current understanding of the TMs and the NHSE but also open new grounds for topological applications.

拓扑模式 (TM) 通常位于更大的拓扑晶格^1,2的缺陷或边界处。最近对非厄米特能带理论的研究揭示了非厄米特趋肤效应 (NHSE)，通过该效应，体状态坍缩到边界，成为趋肤模式^3,4,5,6. 在这里，我们探索 NHSE 通过将 TM 的波函数从边界离域来重塑 TM 的波函数。在关键的非厄米参数下，间隙内 TM 甚至在整个体晶格中完全扩展，形成“连续体外的扩展模式”。这些扩展模式仍然受到体带拓扑的保护，使其能够抵抗局部紊乱。TM 波函数的变形是在一维和二维拓扑晶格以及高阶拓扑晶格中的活动机械晶格中通过实验实现的。此外，通过非隐性分布的明智工程，TM 可以变形为多种形状。我们的发现不仅拓宽和加深了当前对 TM 和 NHSE 的理解，而且还为拓扑应用开辟了新的领域。