The reciprocating and bipolar non-Hermitian skin effect engineered by spin–orbit coupling

Abstract

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.