Effective Hamiltonian for Photonic Topological Insulator with Non-Hermitian Domain Walls

The gain and loss in photonic lattices provide possibilities for many functional phenomena. In this Letter, we consider photonic topological insulators with different types of gain-loss domain walls, which will break the translational symmetry of the lattices. A method is proposed to construct effective Hamiltonians, which accurately describe states and the corresponding energies at the domain walls for different types of photonic topological insulators and domain walls with arbitrary shapes. We also consider domain-induced higher-order topological states in two-dimensional non-Hermitian Aubry-Andr\'e-Harper lattices and use our method to explain such phenomena successfully. Our results reveal the physics in photonic topological insulators with gain-loss domain walls, which provides advanced pathways for manipulation of non-Hermitian topological states in photonic systems.