Abstract
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.
Highlights
Solitons, solitary waves travelling without changing their shapes, result from the balance between dispersion and nonlinearity
Solitons exist in various nonlinear systems, such as nonlinear optics [1,2,3], BoseEinstein condensates (BECs) [4,5,6,7,8] and Fermi superfluids [9,10,11,12,13,14]
By simulating the dynamics of the circuit, we show that a bright soliton can stably exist in the system
Summary
Solitary waves travelling without changing their shapes, result from the balance between dispersion and nonlinearity. Since topological insulators support lower dimensional edge states, they provide an ideal platform to realize the boundary-localized solitons. Topological phases have been generalized to the higher-order case where gapless edge states are localized at (n − m)dimensional (with m > 1) boundaries [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67]. We theoretically predict the existence of solitons in a 3D second-order topological insulator when nonlinearity is involved Such solitons result from the balance between nonlinearity and dispersion of the hinge modes. E/J the dynamics of the circuit, we show that a bright soliton can stably exist in the system
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