Chirality of Topological Gap Solitons in Bosonic Dimer Chains

We study gap solitons which appear in the topological gap of 1D bosonic dimer chains within the mean-field approximation. We find that such solitons have a nontrivial texture of the sublattice pseudospin. We reveal their chiral nature by demonstrating the anisotropy of their behavior in the presence of a localized energy potential.

Figure 1

(a) Periodic potential of a dimer chain and the corresponding tight-binding representation. (b) Tight-binding dispersion of the dimer chain with the topological gap in the middle for $t=0.9t^{\prime }$.

Figure 2

(a) The energy as a function of variational parameters $a$, $b$ (red, maximum). (b) Potential profile together with the GS (blue curve) and TGS (red curve) density, demonstrating opposite TGS sublattice polarization (red arrows) on two cells (marked in green). (c) The two sublattice pseudospin components ($A$, black; $B$, red) extracted from the full wave function $\psi$. The inset shows the sublattice polarization degree. (d) Potential and the GS (blue curve) and TGS (red curve) wave functions (circles discussed in the text).

Figure 3

(a) Energy of the soliton as a function of its position with respect to the localized potential $\delta (x)$: TGS (gray curve) and GS (blue curve). (b) Soliton trajectories of different families: TGS (black, red, navy, and green curves) and GS (cyan curve).

Figure 4

Soliton trajectories plotted as the particle density as a function of position and time: (a),(b) TGS, oscillating trajectory, or free acceleration, depending on the initial soliton position. (c),(d) Oscillating trajectory of an ordinary GS for the same defect.