Inner non-Hermitian skin effect on the Bethe lattice

We investigate the non-Hermitian Su-Schrieffer-Heeger (SSH) model on the Bethe lattice, revealing a novel localization phenomenon coined the inner non-Hermitian skin effect. This effect is featured by the localization of all eigenstates within the bulk of the lattice, diverging from the conventional skin effect observed in general non-Hermitian systems. The analytical treatment of the model demonstrates that the Hamiltonian can be decoupled into a series of one-dimensional chains, with one end fixed at the bottom boundary while the other ends are positioned at varying generations within the bulk. This configuration leads to the emergence of the inner non-Hermitian skin effect, which is further validated by performing circuit simulations. Our findings provide new insights into the interplay between non-Hermitian physics and the self-similar structure on the Bethe lattice.