Stable higher-order vortex quantum droplets in an annular potential

We address the existence, stability, and evolution of two-dimensional vortex quantum droplets (VQDs) in binary Bose-Einstein condensates trapped in a ring -shaped potential. The interplay of the Lee-Huang-Yang-amended nonlinearity and trapping potential supports two VQD branches, controlled by the radius, width and depth of the potential profile. While the lower -branch VQDs, bifurcating from the system's linear modes, are completely unstable, the upper branch is fully stable for all values of the topological charge m and potential's parameters. Up to m = 12 (at least), stable VQDs obey the anti-Vakhitov-Kolokolov criterion. In the limit of an extremely tight radial trap, the modulational instability of the quasi -1D azimuthal VQDs is studied analytically. We thus put forward an effective way to produce stable VQDs with higher vorticity but a relatively small number of atoms, which is favorable for experimental realization.