Vortex solitons in fractional systems with partially parity-time-symmetric azimuthal potentials

We address the propagation dynamics of topological states in the framework of nonlinear fractional Schrödinger equation modulated by a partially parity-time (PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {PT}$$\end{document})-symmetric azimuthal potential. While the eigenvalue spectra in a PT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {PT}$$\end{document} system experience a symmetry breaking, the pPT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {PT}$$\end{document} system exhibits entirely real spectra. The variation of Lévy index impacts the properties of nonlinear vortex states evidently, including the existence domain, power, and stability. Unlike nonlinear vortices in conservative systems, vortex solitons with opposite charges exhibit different features, due to the nonequivalence of the gain–loss distribution along the azimuthal direction. Linear-stability analysis collaborated with direct numerical propagation simulations demonstrates that stable vortex solitons are possible only when their components are connected as a whole entity. Higher-charged vortex solitons are shown to be more stable than those with lower charges. We, thus, put forward the first example of stable vortex solitons in fractional configurations.