Quantum Hall states of gluons in dense quark matter

Color ferromagnetism of quark matter: A possible origin of a strong magnetic field in magnetars

“…Namely, the stars involve the quark matter with a color magnetic field. The CF phase has been discussed in our previous papers [7,8]. The point of the mechanism is that since a gas of quarks is both colored and electrically charged in the CF phase, observable magnetic field is produced because of its rotation around the color magnetic field.…”

“…Obviously, these two phases are incompatible. Hence we have compared [8] free energies of quarks in each phase in order to find which phase is favored. We have found that the CF phase is more favored than the CS phase at lower baryon chemical potentials.…”

“…Here we consider only the case of ν = 1/2. The detail how the unstable gluons form the quantum Hall state should be addressed to our previous papers [7,8]. ( We have demonstrated the formation of the gluon's quantum Hall states by using Chern-Simons gauge theory, which have been originally applied [15] by us for understanding field theoretically Laughlin states of electrons. )…”

“…We assume for simplicity that all of quarks occupy only the lowest Landau level, that is, Fermi energy µ is less than √ gB. In order to obtain free energies, we notice three conditions [8,18] which must be satisfied in the neutron stars; the conditions of color and electric neutralities, and of beta-equilibrium ( u ↔ d+e − ).…”

“…Thus, the magnetars may involve the quark matter inside their cores. ( We have presented [8] a structure of a neutron star involving both the CF quark matter and nuclear matter by using appropriate equations of state in both matters. ) We have argued that a kind of quantum wells in which quantum Hall states of gluons are present are formed effectively.…”