Non-Hermitian Weyl semimetals:Non-Hermitian skin effect and non-Bloch bulk-boundary correspondence

We investigate novel features of three-dimensional non-Hermitian Weyl semimetals,paying special attention to the unconventional bulk-boundary correspondence.We use the non-Bloch Chern numbers as the tool to obtain the topological phase diagram,which is also confirmed by the energy spectra from our numerical results.It is shown that,in sharp contrast to Hermitian systems,the conventional(Bloch)bulk-boundary correspondence breaks down in non-Hermitian topological semimetals,which is caused by the non-Hermitian skin effect.We establish the non-Bloch bulk-boundary correspondence for non-Hermitian Weyl semimetals:the topological edge modes are determined by the non-Bloch Chern number of the bulk bands.Moreover,these topological edge modes can manifest as the unidirectional edge motion,and their signatures are consistent with the non-Bloch bulk-boundary correspondence.Our work establishes the non-Bloch bulk-boundary correspondence for non-Hermitian topological semimetals.

Topological properties of non-Hermitian Creutz ladders

We study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials,and obtain phase diagrams regarding the presence and absence of an energy gap and in-gap edge modes.The non-Hermitian skin effect(NHSE),which is known to break the bulk-boundary correspondence(BBC),emerges in the system only when the non-Hermiticity induces certain unbalanced non-reciprocity along the ladder.The topological properties of the model are found to be more sophisticated than that of its Hermitian counterpart,whether with or without the NHSE.In one scenario without the NHSE,the topological winding is found to exist in a two-dimensional plane embedded in a four-dimensional space of the complex Hamiltonian vector.The NHSE itself also possesses some unusual behaviors in this system,including a high spectral winding without the presence of long-range hoppings,and a competition between two types of the NHSE,with the same and opposite inverse localization lengths for the two bands,respectively.Furthermore,it is found that the NHSE in this model does not always break the conventional BBC,which is also associated with whether the band gap closes at exceptional points under the periodic boundary condition.