<i>Anti-PT</i> -driven phase transitions in topological dissipative states on metasurfaces

The gapless nature of topological semimetals induces strong bulk-boundary correspondence, significantly enhancing the localization of topological boundary states-a phenomenon that has become a frontier research focus. However, the experimental fabrication challenges of high-dimensional systems limit their integration potential. To address this challenge, this study found an one-dimensional (1D) Weyl-like mode that reduce the dimensionality of high-dimensional topological properties onto a controllable artificial platform, enabled by the introduction of non-Hermitian (NH) characteristics. Specifically, we propose and demonstrate a mechanism for phase transitions in topological dissipative boundary states, synergistically driven by anti-parity-time (anti<i>-PT</i>) symmetry and loss engineering. The criterion for anti<i>-PT</i> symmetry controlled topological phase transitions is established, which not only systematically elucidates the evolution of dissipative boundary states between traditional semimetal states, topological trivial states, and non-trivial states, but also provides a criterion for the 1D Weyl-like modes formation. Furthermore, though the inverse design of optical metasurface, we successfully constructed the NH Hamiltonian and explored the high local performance of 1D Weyl-like modes at the topological dissipative boundary state. This work not only reveals emergent topological dissipative boundary states induced by anti<i>-PT</i> symmetry but also achieves precise inverse design and control of complex non-Hermitian coupling coefficients on the metasurface, thereby opening a new way for the active manipulation of on-chip topological photonic devices.