Unconventional skin modes in generalized topolectrical circuits with multiple asymmetric couplings

Abstract

The eigennmodes in a non-Hermitian system containing nonreciprocal couplings may exhibit an extreme localization, also known as non-Hermitian skin effect (NHSE), under open boundary conditions. Here, we ex- plore unconventional scenarios where the interplay between multiple asymmetric couplings can cause the NHSE to vanish, unlike in known models with nonreciprocal couplings, where the NHSE vanishes only when the non-Hermiticity is turned off. We derive general conditions for the NHSE in a non-Hermitian superlattice in which the overall eigenmode localization is determined by the geometric mean of the cumulative contributions of all asymmetric coupling segments. In the limit of large unit cells, our results provide a route towards the NHSE caused by asymmetric hopping textures, rather than single asymmetric hoppings. We provide explicit electrical circuit setups for realizing our observations, which also extend to other established platforms such as photonics, mechanics, and optics systems, and quantum circuits.