Fig. 4: Co-existence of the scale-free accumulation (SFA) and the non-Hermitian skin effect (NHSE).
a–c Decaying exponents κL and κOBC(k) of the SFA and NHSE, respectively, for the Hamiltonian of Eq. (5) with different boundary impurities μ. d–f Their corresponding spectra under different parameters and different boundary conditions. The blue lines, blue circles, and gray dots in d–f correspond to the spectra of the SFA with eigenenergy given by E = ϵ(k + iκL), numerical results with a boundary impurity, and the NHSE where E = ϵ(k + iκOBC(k)) respectively, with ϵ(k) the eigenenergy under periodic boundary conditions. The system’s parameters are α = 1, L = 80, and μ = e−30, e−45, and e−60 from left to right.
