Non-Hermitian winding and braiding of topological boundary states

Topological boundary state is the hallmark feature of topological physics. Recently, non-Hermicity was found to dramatically expand the scope of topological physics, and provides an exotic strategy to manipulate the topological boundary states. Here, we realize the non-Hermitian winding and braiding of topological edge states in electric circuits. The topological edge states originate from the nontrivial bulk polarization. The twisted winding of a topological edge band and the ensuing bipolar hybrid skin-topological effect, and the Hopf link and Solomon link braidings between two topological edge bands, are visualized by measuring the admittances in circuit experiments. Our findings deepen the insight into the interaction between the Hermitian and non-Hermitian topologies, and inspire a mechanism in topological boundary wave manipulation.