Interaction-induced second-order skin effect

In contrast to the conventional (first-order) non-Hermitian skin effect (NHSE) in a $d$-dimensional system with linear size $L$, the $n\mathrm{th}$-order (higher-order) NHSE is characterized by skin modes localized at lower-dimensional boundaries of dimension $(d\ensuremath{-}n)$. The total number of these modes scales linearly with the system size $L$. Significant progress has been made in understanding higher-order NHSE in noninteracting systems. In this work, we demonstrate the many-body interaction-induced second-order skin effect in a two-dimensional non-Hermitian bosonic system. Specifically, we construct a square lattice that incorporates nonreciprocal single-boson hopping, on-site many-body interactions, and two-boson pairing hopping. In the absence of interactions, no second-order NHSE is observed. However, with the inclusion of interactions, we identify interaction-induced skin modes for in-gap doublon states (i.e., bound pairs of bosons) localized at the corners of the lattice, while the bulk doublon states remain extended. These corner-localized skin modes arise from the interplay between interaction-induced edge states, localized along one-dimensional boundaries, and the nonreciprocal hopping along these boundaries. Furthermore, the number of corner skin modes scales linearly with the system size, confirming the presence of second-order NHSE in this interacting system. Our findings introduce an approach to realizing higher-order skin effects by leveraging interactions.