Vortices in $\mathcal {PT}$-symmetric non-Hermitian two-component superfluid

We discuss vortex solutions in the non-Hermitian parity-time-symmetric relativistic model with two interacting scalar complex fields. In the London limit, the vortex singularities in different condensates experience dissipative dynamics unless they overlap. At finite quartic couplings, the vortices appear in the PT-symmetric regions with broken U(1) symmetry. We find the phase diagram of the interacting model where the PT-symmetric and PT-broken regions together with the U(1)-symmetric and U(1)-broken phases form complicated patterns.