Vector solitons in parity-time-symmetric mixed linear-nonlinear lattices with fractional diffraction

We demonstrate that \mathcalPT-symmetric mixed linear-nonlinear lattices can sustain mixed-gap vector solitons in the coupled nonlinear Schrödinger equations with fractional diffraction. Here, mixed-gap vector solitons refer to solitons whose first and second components exist in different band gaps. In this work, the first component is a fundamental soliton, while the second is a dipole. When the propagation constant of the first component is fixed, the soliton power of the first component decreases as the propagation constant of the second component increases. Conversely, the power of the second component increases with its own propagation constant. We study cases with both large and small values of the Lévy index. We also study the stability of these solitons, using linear stability analysis and perturbed propagations. Interestingly, the stability domains of vector solitons with a large Lévy index are consistently much wider than those with a small Lévy index.