Exploring topological phases in non-Hermitian systems has attracted significant recent attention. One intriguing question is how topological edge states compete with the non-Hermitian skin effect. Here we report the experimental observation of corner states in a two-dimensional nonreciprocal rhombus honeycomb electric circuit. We construct nonreciprocal and non-Hermitian circuits by introducing current-direction resolved capacitance between two nodes depending on the current direction. A skin effect thus emerges due to the nonreciprocity and prevails in dragging the corner state into the bulk. The non-Bloch winding number defined in the generalized Brillouin zone is adopted to characterize the topological phase transition. Interestingly, we find that the non-Bloch $Z_2$ Berry phase can serve as an invariant to describe the non-Hermitian topology. By tuning the nonreciprocal parameter, we observe unbalanced distribution of corner states emerging on two acute angles of the rhombus lattice, with the localization length of the left corner state increasing exponentially with the degree of nonreciprocity.

• Received 23 December 2022
• Revised 21 June 2023
• Accepted 1 July 2023

DOI:https://doi.org/10.1103/PhysRevB.108.035410