Topological funneling effect in electrical circuits

In recent decades, topology in condensed matter systems has become a central focus of research in physics. Although we are trained to think about Hermitian systems with the energy being observable and always assuming real values, there is also significant enthusiasm for non-hermitian (NH) systems. The fortuitous interplay between topology and non-hermiticity has unveiled an array of fascinating physical phenomena, notably the non-Hermitian skin effect (NHSE), wherein the bulk eigenstates predominantly localize near the system boundaries. In 2020, S. Weidemann et al. demonstrated the NHSE in a photonic mesh lattice by adjusting the anisotropy of the nearest-neighbor coupling, a phenomenon called the "topological funneling of light," also dubbed the funnel effect. The research presented here highlights how the properties of NH systems, rather than being an unavoidable nuisance, can be harnessed and applied in sophisticated photonics applications. Another theoretical work by Z. Turker and C. Yuce recently explored the NH jump and the topological funneling effect in the Hatano-Nelson (HN) model. This study considered an NH lattice described by the HN model with oppositely signed couplings to investigate NH transport phenomena. However, aside from optical setups, these systems have yet to be realized in any other experimental framework. In this work, we aim to extend the study of NH phenomena, such as the topological funnel effect and NH jumps, into a new experimental platform using topolectrical circuits (TECs). We demonstrate these effects both theoretically and through simulations in LTspice, providing a realistic framework for electrical circuit networks. Additionally, we explore the impact of quasi-periodic disorder on these phenomena, revealing intriguing new insights into the interplay between non-Hermiticity and randomness. These findings open the door to potential applications in advanced electronics and beyond.