Recently it was shown that vacuum in a background of a 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 ${\rho }^{(0)}$ 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 superconductor and superfluid vortex lattices has a honeycomb pattern.

• Received 29 November 2011

DOI:https://doi.org/10.1103/PhysRevD.85.045002