Topological semimetal phase in non-Hermitian Su-Schrieffer-Heeger model

We explore the non-Hermitian Su-Schrieffer-Heeger model with long-range hopping and off-diagonal disorders. In the non-Hermitian clean limit, we find that the phase diagram holds topological semimetal phase with exceptional points except the normal insulator phase and the topological insulator phase. Interestingly, it is found that the topological semimetal phase is induced by long-range nonreciprocal term when the long-range hopping is not equal to the intercell hopping. Especially, we show the existence of topological semimetal phase with exceptional points and determine the transition point analytically and numerically under the Hermitian clean limit when the long-range hopping is equal to the intercell hopping. Furthermore, we also investigate the effects of the disorders on topological semimetal phase, and show that the disorders can enhance the region of topological semimetal phase in contrast to the case of non-Hermitian clean limit, indicating that it is beneficial to topological semimetal phase whether there is one disorder or two disorders in the system, that is, the topological semimetal phase is stable against the disorders in this one-dimensional non-Hermitian system. Our work provides an alternative avenue for studying topological semimetal phase in non-Hermitian lattice systems.