Nth power root topological phases in Hermitian and non-Hermitian systems

Abstract

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 $N\mathrm{th}$ 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.