Topology in non-Hermitian Chern insulators with skin effect

The non-Hermitian skin effect can arise in materials that have asymmetric hoppings between atoms or resonating units, which makes the bulk eigenspectrum sensitive to boundary conditions. When skin effect emerges, eigenstates in the bulk continuum can become localized on the edges, making the distinction between edge and bulk states challenging. We establish the bulk-boundary correspondence for a Chern insulator model with non-Hermitian skin effect by combining two approaches (non-Bloch approach and biorthogonal approach). Both approaches can suppress the skin effect but they are based on different mathematical tools. A biorthogonal inverse participation ratio is used as a measure to distinguish between bulk states and edge states, and a non-Bloch Chern number is used to characterize the topology and predict the number of topological edge bands. In addition to tangential degeneracies, crossing degeneracies are found to occur between the bulk and edge bands. Their presence enriches the (de)localization behavior of the edge states but does not affect the Chern number. The phase diagram of the system has interesting features that are not found in Hermitian systems. For example, one topological transition and two non-Hermitian phase transitions can be induced by tuning a single parameter. The gapless phase is topologically protected due to the stable existence of the non-Hermitian band degeneracies guaranteed by nonzero discriminant numbers.

Automated summary

This study investigates the bulk-boundary correspondence in a Chern insulator model with non-Hermitian skin effect, using the biorthogonal approach and non-Bloch approach to suppress the skin effect. The biorthogonal inverse participation ratio and non-Bloch Chern number are utilized as metrics and tools for predicting topological features. Moreover, the occurrence of crossing degeneracies between bulk and edge bands enriches the localization behavior of edge states.