Nested chirality and multimode transfer around exceptional points driven by external forces in electric circuits

Exceptional points (EPs) are non-Hermitian degeneracies or branch points where eigenvalues and their corresponding eigenvectors coalesce. Due to the complex non-trivial topology of Riemann surfaces associated with non-Hermitian Hamiltonians, the dynamical encirclement or proximity of EPs in parameter space has been shown to lead to some novel physical phenomena, such as the chiral modes modulations. However, in the previous studies on dynamically encircling EPs, tuning the chirality for applications requires periodic modulation of the system parameters. Here, we propose theoretically and demonstrate experimentally a way to generate EPs and realize asymmetric multimode switching by tuning external forces. The application of the external force achieves the effect of modifying the system parameters so that the dynamical encircling of the EPs can be easily realized. It is shown theoretically that nested chiral behavior and multimode transfer appear in a two-dimensional non-Hermitian higher-order topological insulator with twofold degenerate second-order EPs by tuning the external forces. Furthermore, we design and fabricate the corresponding circuit networks, and experimentally observe nested chiral behavior and multimode transfer. Our work opens up avenues for practical applications of the non-Hermitian physical phenomena. Encircling exceptional points (EPs) in non-Hermitian Hamiltonians has brought up many exotic physical phenomena. This work demonstrates a way to realize asymmetric multimode switching around EPs by applying external forces, with the disclosed nested chirality, which can open the path towards the dynamical tuning of non-Hermitian systems.