The Reciprocating and Bipolar Non-Hermitian Skin Effect Engineered by Spin–orbit Coupling

We theoretically study a one-dimensional non-Hermitian Su-Schrieffer-Heeger model with an imaginary gauge field and spin-orbit coupling. We find that, under open boundary conditions, the dispersions possess the reciprocating real-complex-real transitions with increasing the strength of spin-orbit coupling. Correspondingly, the bulk energy eigenstates exhibit a reciprocating non-Hermitian skin effect. This mechanism can be characterized by the generalized Brillouin zone moduli, which approaches zero or infinity at the transition points. We further demonstrate the non-zero winding number inside the loops of generalized Brillouin zone when the strength of intra-cell spin-orbit coupling is larger than the inter-cell one, which results in the bipolar non-Hermitian skin effect. As the intra-cell and inter-cell spin-orbit coupling strength becomes comparable, the bipolar non-Hermitian skin effect degenerates to the conventional non-Hermitian skin effect. Our work may pave the way for the non-Hermitian optoelectronic devices utilizing the reciprocating non-Hermitian skin effect and the bipolar non-Hermitian skin effect by engineering the spin-orbit coupling.