Realization of non-Hermitian Hopf bundle matter

Non-trivial linking invariant encodes robust information of topological matter. It has been recently shown that the linking and winding of complex eigenenergy strings can classify one-dimensional non-Hermitian topological matter. However, in higher dimensions, bundles of linked strings can emerge such that every string is mutually linked with all the other strings. To the best of our knowledge, a non-Hermitian Hopf bundle has not been experimentally clarified. Here, we attempt to explore the non-Hermitian Hopf bundle by visualizing the global linking structure of spinor strings in the momentum space of a two-dimensional electric circuit. By exploiting the flexibility of reconfigurable couplings between circuit nodes, we study the non-Hermitian topological phase transition by exploring the intricate structure of the Hopf bundle. Furthermore, we find that the higher-order skin effect in real space is accompanied by the linking of spinor strings in momentum space, revealing bulk-boundary correspondence between the two domains. all The authors employ topolectric circuits to realize a non-Hermitian topological Hopf bundle state of matter, which allows them to observe the emergence of phases that are unique to non-Hermitian systems. The proposed non-Hermitian Hopf bundle platform and visualization methodology pave the way for designing new topologically robust non-Hermitian phases of matter.