Hybrid skin-topological modes without asymmetric couplings

The non-Hermitian skin effect (NHSE) in non-Hermitian lattice systems, associated with a point gap on the complex energy plane, has attracted great theoretical and experimental interest. Much less is studied on the so-called second-order non-Hermitian skin effect, where the bulk does not support a point gap but localization at the corner still occurs. This work discovers a class of hybrid skin-topological modes as the second-order non-Hermitian skin effect without asymmetric couplings. Specifically, by only adding gain/loss to two-dimensional Chern insulators and so long as the gain/loss strength does not close the line gap, all the topological edge states are localized at one corner under the open boundary condition, with the bulk states extended. The resultant non-Hermitian Chern bands can be still topologically characterized by Chern numbers, whereas the hybrid skin-topological modes are understood via some auxiliary Hermitian systems that belong to either intrinsic or extrinsic second-order topological insulator phases. By proposing an innovative construction of auxiliary Hamiltonian, our generic route to hybrid skin-topological modes is further successfully extended to nonequilibrium topological systems with gain and loss, where the anomalous Floquet band topology is no longer captured by band Chern numbers. The extension thus leads to the intriguing finding of nonequilibrium hybrid skin-topological modes. In addition to offering a straightforward route to experimental realization of hybrid topological-skin effects, this study also opens up a promising perspective for the understanding of corner localization by revealing the synergy of three important concepts, namely, non-Hermitian topological insulator, second-order non-Hermitian skin effect, and second-order topological insulator.