  We explore vortices in non-equilibrium Dirac Bose-Einstein condensates (Dirac
BEC) described by a stationary Dirac Gross-Pitaevskii equations (GPE). We find
that the multi-component structure of Dirac equation enables the difference in
phase winding of two condensates with respective phase winding number differing
by one, $\ell_a - \ell_b = \pm 1$. We observe three classes of vortex states
distinguished by their far-field behavior: A ring soliton on either of the two
components in combination with a vortex on the other component, and, in the
case of strong inter-component interactions, a vortex profile on both
components. The latter are multiple core vortices due to the phase winding
difference between the components. We also address the role of a Haldane gap on
these vortices, which has a similar effect than inter-component by making the
occupation on either sublattice more costly. We employ a numerical shooting
method to reliably identify vortex solutions and use it to scan large parts of
the phase space. We then use a classification algorithm on the integrated
wavefunctions to establish a phase diagram of the different topological
sectors.
