A Non-Abelian Route to Z2 Non-Hermitian Skin Effects

Abstract

The non-Hermitian skin effect (NHSE), characterized by extensive boundary accumulation of eigenstates under open boundary conditions, has emerged as a central phenomenon in non-Hermitian physics. Conventionally, the NHSE arises from either non-reciprocal couplings or onsite gain and loss combined with synthetic gauge fields. Existing studies, however, have been largely confined to frameworks with Abelian-coupling, leaving the role of non-Abelian couplings essentially unexplored. Here, we demonstrate that non-Abelian-couplings can generate the NHSE, giving rise to a time-reversal-symmetry-protected Z2 skin effect with pseudospin-dependent boundary localization and dynamical pseudospin separation. Experimentally, we implement a representative four-level model using a programmable topolectrical circuit and directly observe both the predicted NHSE and the boundary-induced pseudospin-inversion reflection. Our work establishes a fundamental link between non-Abelian coupling and non-Hermitian topology, opening new avenues for realizing non-reciprocity-free topological materials and devices.