Topological energy braiding of the non-Bloch bands

The non-Hermitian skin effect, as a unique feature of non-Hermitian systems, will break the topological energy braiding of the Bloch bands in open boundary systems. Going beyond the Bloch band theory, we unveil the energy braiding of the non-Bloch bands by introducing a one-dimensional non-Hermitian tight-binding model. We find an entirely new generic class of topological non-Bloch bands such as Hopf link, which is generally generated by the non-Hermitian skin effect. The energy braiding is topologically robust against any perturbations without gap closing. Furthermore, non-Bloch topological invariants are proposed based on the generalized Brillouin zone to characterize the topology of these non-Bloch bands. The topological phase transition between the distinct phases occurs with the non-Bloch bands touching at exceptional points. We hope that our work can shed light on the topological energy braiding of the non-Bloch bands for non-Hermitian systems.