Supersymmetric non-Hermitian topological interface laser

We investigate laser emission at the interface of the topological and trivial phases in one dimension. The system is described by a generalized Su-Schrieffer-Heeger model with site-dependent hopping parameters involving the interface width parameter where gain (loss) is introduced only to the A (B) sites of the bipartite lattice. The topological interface state is described by the Jackiw-Rebbi state with a pure imaginary energy, reflecting the non-Hermiticity of the system. It feels only the gain effect since it is strictly localized at the A sites. The Jackiw-Rebbi state exists for any value of the interface width. We, thus, obtain a large area single-mode laser by making the interface width wide enough. We also find a series of analytic solutions of excited states based on supersymmetry (SUSY) quantum mechanics where the A and B sites of the bipartite lattice form SUSY partners. Furthermore, we study the system containing loss and gain with saturation by extending the Jackiw-Rebbi mode to a nonlinear theory.