Electromagnetically superconducting phase of vacuum in strong magnetic field: structure of superconductor and superfluid vortex lattices in the ground state

Recently it was shown that vacuum in a background of strong enough magnetic field becomes an electromagnetic superconductor due to interplay between strong and electromagnetic forces. The superconducting ground state of the vacuum is associated with a spontaneous emergence of quark-antiquark condensates which carry quantum numbers of charged rho mesons. The rho-meson condensate is an inhomogeneous structure made of the so-called rho vortices, which are parallel to the magnetic field axis. The condensation of the charged rho mesons induces a (much weaker) superfluid-like condensate with quantum numbers of the neutral rho mesons. In this paper we show that the vortices in the superconducting condensate organize themselves in an equilateral triangular lattice similarly to an ordinary type-II superconductor. We show that each of these superconductor vortices is accompanied by three superfluid vortices and three superfluid antivortices made of the neutral rho meson condensate. The superconductor vortex overlaps with one of the superfluid vortices. The superposition of the superconducting and superfluid vortex lattices has a honeycomb pattern.