Fig. 1: First-order non-Hermitian (NH) skin effect on a square lattice and Sierpinski carpet (SC) fractal.
From: Inner skin effects on non-Hermitian topological fractals
a Total weight of all the left eigenvectors (normalized by its maximum value) of HFO [Eq. (1)] on a square lattice with open boundary condition (OBC), displaying NH skin effect at outer left edge. b Same as a but with periodic boundary condition (PBC) in the x direction, showing no skin effect. c Same as a, but on a SC fractal of third generation (containing 512 sites) with OBC, showing NH skin effect at its outer left edge. d Same as c, but with PBC only in the x direction, confirming the proposed NH inner skin effect at its inner left edges. The outcomes in b and d remain qualitatively unchanged with additional PBC in the y direction. Here we set m0 = 0, h = (0.4, 0, 0), t = t0 = 1, r0 = a, and R = 2a, where a is the distance between the nearest-neighbor sites [Eq. (2)]. For right eigenvectors the skin effect appears on the right edges. See Supplementary Fig. 1.
