Only hybrid anyons can exist in broken symmetry phase of nonrelativistic U(1)² Chern-Simons theory

We present two examples of parity-invariant $[U(1)]^{2}$ Chern-Simons-Higgs models with spontaneously broken symmetry. The models possess topological vortex excitations. It is argued that the smallest possible flux quanta are composites of one quantum of each type $(1,1)$. These hybrid anyons will dominate the statistical properties near the ground state. We analyse their statistical interactions and find out that unlike in the case of Jackiw-Pi solitons there is short range magnetic interaction which can lead to formation of bound states of hybrid anyons. In addition to mutual interactions they possess internal structure which can lead upon quantisation to discrete spectrum of energy levels.