N th power root topological phases in Hermitian and non-Hermitian systems

Constructing new topological phases is very important in both Hermitian and non-Hermitian systems because of their potential applications. Here we propose theoretically and demonstrate a general scheme experimentally to construct Nth power root topological phases. Such a scheme is not only suitable for Hermitian systems, but also non-Hermitian systems. It is found that the robust degree of edge state in the Hermitian system becomes stronger and stronger with the increase of N. It tends to be a strongly surface localized form when N is large enough. In the non-Hermitian system, the skin effect becomes more apparent, and it approaches the ideal situation with the increase of N. This means that edge states and skin effects can be observed by taking different N. This scheme has been proved experimentally by designing circuits. Our work opens up a way to engineer topological states according to the requirements, which is very important for developing topologically protected devices, such as topology sensing, switches, and so on.