Evolution of topological extended state in multidimensional non-Hermitian topolectrical circuits

The extended state pertains to the dispersion of the system's eigenfunctions across the whole lattice. Recent studies have shown that the non-Hermitian skin effect (NHSE) can reshape the wavefunction of topological modes. The localized states of topological modes within the bandgap gradually delocalized into extended states through the manipulation of NHSE. Here, we clarify the NHSE direction using the Bloch spectral winding numbers and reestablish the bulk-boundary correspondence through the non-Bloch winding numbers in the generalized Brillouin zone. We elucidate the formation of extended state by employing the localized decay length. Then, we have designed non-Hermitian topological circuits for experimental verification based on the voltage follower. The corner states, edge states, and extended states in 1D, 2D, and 3D circuits were observed through the measurement of node voltage. Our work can achieve the sustainable extended mode and provides significant cases for the analysis of topolectrical circuits.