Vortex Excitations in Dirac Bose-Einstein Condensates

We explore vortices in non-equilibrium Dirac Bose-Einstein condensates (Dirac BEC) described by a multi-component Gross-Pitaevskii equation. We find that the linear kinetic energy of the Dirac equation enables a difference in phase winding of the two condensate components. We observe three classes of vortex states distinguished by their far-field behavior: A locally constrained ring soliton on either of the two components in combination with a vortex profile on the other component, and a vortex profile on both components if inter-component interactions are sufficiently strong. We also address the role of a Haldane gap on these vortices, which encourages the occupation of the component with the larger winding number, and thereby facilitates the creation of the dual vortex state. We employ a numerical shooting method to identify vortex solutions and use it to scan large parts of the parameter space. A classification algorithm on the integrated wavefunctions allows us to establish a phase diagram of the distinct vortex states in Dirac BEC.