Internal modes of two-dimensional quantum droplets

We address the effects of internal modes on the evolution dynamics of quantum droplets in symmetric binary Bose-Einstein condensates. Angle-dependent internal modes and the corresponding eigenvalues are solved numerically for both fundamental droplets and vortex droplets with different topological charges. When internal modes corresponding to the largest eigenvalues are excited, perturbed droplets are deformed and appear as regular polygons. While neutrally internal modes make the evolution of a droplet like a breather, the internal modes with higher angular indices result in a persistently periodic rotation of droplets.