Stabilization of zero-energy skin modes in finite non-Hermitian lattices

The zero energy of a one-dimensional semi-infinite non-Hermitian lattice with nontrivial spectral topology may disappear when we introduce boundaries to the system. While the corresponding zero-energy state can be considered as a quasi-edge state for the finite lattice with a long survival time, any small disruption (noise) in the initial form of the quasi-edge state can significantly shorten the survival time. Here, by tailoring the couplings at one edge we form an exceptional point allowing for a topological phase transition and the stabilization of the quasi-edge state in a finite-size lattice with open edges. Such a small modification in the lattice does not require closing and opening of the band gap and opens the door for experimental realization of such robust zero-energy edge states.