  We investigate the phase structure of two-component Bose-Einstein condensates
(BECs) with repulsive intra- and interspecies interactions in the presence of
respective vortex-antivortex superposition states (VAVSS). We show that
different winding numbers of vortex and antivortex and different intra- and
interspecies interaction strengths may lead to different phase configurations,
such as fully separated phases, inlaid separated phases, asymmetric separated
phase, and partially mixed phases, where the density profile of each component
displays a petal-like (or modulated petal-like) structure. A phase diagram is
given for the case of equal unit winding numbers of the vortex and antivortex
in respective components, and it is shown that conventional criterion for phase
separation of two-component BECs is not applicable for the present system due
to the VAVSS. In addition, our nonlinear stability analysis indicates that the
typical phase structures of two-component BECs with VAVSS allow to be detected
in experiments. Moreover, for the case of unequal winding numbers of the vortex
and antivortex in respective components, we find that each component in any of
the possible phase structures is in a cluster state of vortices and
antivortices, where the topological defects appear in the form of singly
quantized visible vortex, or hidden vortex, or ghost vortex, depending on the
specific parameters of the system. Finally, a general rule between the
vortex-antivortex cluster state and the winding numbers of vortex and
antivortex is revealed.
