Nonlinear Topological Laser on the Non-Hermitian Haldane Model with Higher-order Corner States

The non-Hermitian skin effect (NHSE) on the non-Hermitian Haldane model with gain and loss on the honeycomb lattice with the outline of a triangle is discussed. The NHSE only occurs on the edge of the lattice, transforming the edge modes into the higher-order corner modes. The NHSE can also occur on a lattice with only loss, which can be treated as a lattice with gain and loss as well as a global loss added to it. When the saturated gain is added to the three corner sites of the dissipative lattice, a single-mode laser system is obtained. When any one site is stimulated initially, the system will reach a saturated state depending on the distribution of the corner modes, and the stable laser light is emitted by sites at the corners.