Higher-Order States in a Non-Hermitian 3D Topological Photonic Crystal

Higher-order topological insulators hosting topological modes at hinges and corners provide a new avenue for disorder-immune light transport, which prospects great potential in applications of integrated photonics devices. However, the active control of topological modes in 3D higher-order topological insulators is not realized yet, and its construction is too complicated and huge to analyze. Here, a method is proposed to construct effective Hamiltonians for higher-order topological insulators, which provides a correct physical picture of the states and the corresponding energies at the domain walls. A non-Hermitian 3D honeycomb lattice is constructed, which can generate arbitrary-located, arbitrary-shaped, and robust topological hinge states propagating at gain-loss domain walls. The 3D honeycomb lattice can also appear as non-Hermitian third-order TIs exhibiting corner states, which can be dynamically controlled and show new topologically protected confinement rules. This work expands the understanding of the topological properties in non-Hermitian systems and enables the dynamic control of topological states of different dimensions. A method is proposed to construct effective Hamiltonians describing states and the corresponding energies at the gain-loss domain walls for higher-order topological insulators. Non-Hermitian 3D topological photonic crystals generating arbitrary-located, arbitrary-shaped, and robust topological hinge states propagating at gain-loss domain walls are constructed, which can be actively controlled by non-Hermiticity.image