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Abstract
Matter in nontrivial topological phase possesses unique properties, such as support of unidirectional edge modes on its interface. It is the existence of such modes which is responsible for the wonderful properties of a topological insulator – material which is insulating in the bulk but conducting on its surface, along with many of its recently proposed photonic and polaritonic analogues. We show that exciton-polariton fluid in a nontrivial topological phase in kagome lattice, supports nonlinear excitations in the form of solitons built up from wavepackets of topological edge modes – topological edge solitons. Our theoretical and numerical results indicate the appearance of bright, dark and grey solitons dwelling in the vicinity of the boundary of a lattice strip. In a parabolic region of the dispersion the solitons can be described by envelope functions satisfying the nonlinear Schrödinger equation. Upon collision, multiple topological edge solitons emerge undistorted, which proves them to be true solitons as opposed to solitary waves for which such requirement is waived. Importantly, kagome lattice supports topological edge mode with zero group velocity unlike other types of truncated lattices. This gives a finer control over soliton velocity which can take both positive and negative values depending on the choice of forming it topological edge modes.
Highlights
Various physical systems often demonstrate similarity in the underlying physical phenomena
Operators ai†,σ create exciton-polariton of circular polarization σ = ± at site i of the kagome lattice, the summation ij is over nearest neighbors (NN), angles φij specify directions of vectors connecting the neighboring sites
The first term in (1) describes the Zeeman energy splitting (2 Ω) of the circular polarized components induced by external magnetic field, the second term describes the NN hopping with conservation and inversion of circular polarization, and the last term describes the on-site polariton-polariton interactions with effective constants α1 and α2 defined for the given pillar mode
Summary
While the effect of Ω on the band structure is to shift energy dispersions of the two circular polarization by the amount of Zeeman splitting, the non-zero δJ results in coupling of the two circular polarizations and an anticrossing of the corresponding dispersion curves. The sign of the group velocity of edge states propagating along the “uncoupled” boundary (the bottom one on Fig. 1a) can be reversed, see Fig. 1b Such highly nonlinear dispersion turns out to be favorable for the existence of nonlinear excitations of TEM in the form of solitons. For the amplitude A(κ, t) to choose a gauge be uniquely such that the defined, one equation needs to fix a gauge of the basis vectors ukσ,ne
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