Third Chern Topology in Hexeract Circuits

ABSTRACT

When the system dimension breaks through the three‐dimensional (3D) physical space and enters the synthesis dimension of four‐dimensional (4D), six‐dimensional (6D), or even higher, the topological invariants become the mathematical law to describe the global nature in the extremely complex parameter maze. Here, we explore the third Chern topology in an explicitly constructed 6D electric circuit lattice. To reduce the prohibitive computational costs of high‐dimensional tensor calculations inherent in conventional 6D topological evaluations, our design utilizes the steady‐state admittance spectrum as a direct physical proxy. By modularizing hopping channels into scalable reactive couplings, we drastically reduce network complexity. This streamlined architecture enables the reproducible assembly of finite‐size Hexeract lattices and direct observation of mass‐driven phase transitions and robust corner states, establishing a highly efficient paradigm for high‐dimensional topological physics.