Topological phase transition and bipolar skin effect in the Su-Schrieffer-Heeger chain with nonreciprocal spin-orbital coupling

We concentrate on the topological phase transition and non-Hermitian skin effects in a spinful Su-Schrieffer-Heeger (SSH) chain by considering the presence of nonreciprocal spin-orbital coupling (NSOC). Via performing combined similarity and unitary transformation, this SSH chain is reconstructed as two nonreciprocal SSH subchains. Then, the global physical properties of this system are determined by discussing the two subchains. It is found that the system displays the topologically trivial-to-nontrivial phase transition, and the NSOC plays nontrivial roles in governing the non-Hermitian skin effect and pseudo-Hermitian symmetric phase transition. Moreover, the bipolar skin effect is allowed to come into being, with the different localization properties on the two sides of the chain. It can be believed that the findings in this work promote to understand the topological edge states and skin effects in the SSH lattices with non-Hermitian NSOCs.