Hybrid skin-topological modes without asymmetric couplings

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