Skin effect protected by custodial chiral symmetry

The non-Hermitian skin effect is a unique feature of non-Hermitian systems, in which an extensive number of boundary modes appear under open boundary conditions. It has been determined that this effect originates from intrinsic non-Hermitian topology protected by spatial symmetry or particle-hole symmetry. Here, we reveal another kind of skin effect which is protected by custodial chiral symmetry. Custodial chiral symmetry is common in the standard model of particle physics. Recent investigations have shown that such symmetry is also present in a classical Su-Schrieffer-Heeger electrical circuit with memory. We extend this discussion to non-Hermitian systems. It is shown that the skin effect can appear through the introduction of memristors that break the conventional chiral symmetry while giving rise to an emergent custodial chiral symmetry. This skin effect protected by custodial chiral symmetry, along with the associated topological edge states, enables tunable non-Hermitian topological behavior and exhibits strong robustness against perturbations.