Hinge solitons in three-dimensional second-order topological insulators

Higher-order topological insulators have recently witnessed rapid progress in various fields ranging from condensed matter physics to electric circuits. A well-known higher-order state is the second-order topological insulator in three dimensions with gapless states localized on the hinges. A natural question in the context of nonlinearity is whether solitons can exist on the hinges in a second-order topological insulator. Here we theoretically demonstrate the existence of stable solitons localized on the hinges of a second-order topological insulator in three dimensions when nonlinearity is involved. By means of systematic numerical study, we find that the soliton has strong localization in real space and propagates along the hinge unidirectionally without changing its shape. We further construct an electric network to simulate the second-order topological insulator. When a nonlinear inductor is appropriately involved, we find that the system can support a bright soliton for the voltage distribution demonstrated by stable time evolution of a voltage pulse.