Complex–Real Transformation of Eigenenergies and Topological Edge States in Square‐Root Non‐Hermitian Topolectrical Circuits

The physical properties of the unconventional complex–real transformation of eigenenergies which is manifested by the multiple degenerate plat bulk bands in the energy spectrum and the topological properties characterized by robust edge states are investigated in the square‐root non‐Hermitian topolectrical circuits. Such a flat bulk band captures all the imaginary eigenenergies of the system, which also determines its destiny as an indicator of complex–real transformation. In addition, its degeneracy is twice the number of unit cells and its possible generation mechanism has also been explored. The existence of robust topological edge states with non‐zero real energy is hinted by a strong impedance resonance peak displayed on the boundary in a modified disordered circuit system. The non‐Bloch theorem is introduced to renovate the broken bulk‐boundary correspondence confirmed by theoretical analysis and numerical calculations. Finally, the entire phase diagram of the system is presented to perfectly show all the intriguing physics. This work further enriches the study of physical characteristics and other exotic topological phenomena on an accessible electronic circuit platform. The complex–real transformation of eigenenergies and the topological edge states are investigated in square‐root non‐Hermitian topolectrical circuits. The complex–real transition is determined by the fate (presence or absence) of the flat bulk band characterized by all imaginary eigenenergies. The non‐Bloch winding number is introduced to complete the construction of the system phase diagram.