Topological states in a five-dimensional non-Hermitian system

Revealing new topological phases is of utmost importance in both Hermitian and non-Hermitian systems due to their potential applications. Generally, topological phases depend on the dimension of the system. Previous studies have shown that five-dimensional (5D) Hermitian systems exhibit certain phases that are not supported by their lower-dimensional counterparts. Here, we investigate the topological properties of 5D non-Hermitian systems and discover topological phases, such as Yang monospheres, Fermi cylinder surfaces, Fermi arcs connecting the two Yang monospheres, and the 5D skin effect. The topological invariants characterizing these phases can be described by both the second Chern number and a quantized Berry phase of the Yang monosphere. Additionally, we conduct experiments on the circuit platform to experimentally confirm the existence of these topological phases. Our findings also leverage the concept of higher-dimension non-Hermitian Weyl physics to control electrical signals in the engineered circuits.