Coexistence of magnetic and charge order in a two-component order parameter description of the layered superconductors

A two-component order parameter approach for the layered superconductor is shown to form a condensate with magnetic and charge degrees of freedom. This condensate is an inhomogeneous state, topologically stable, that exists without the presence of an applied magnetic field. We show that the charge density in the layers presents hexadecapole moment in its lowest order. Our approach is based on the first order equations that we show here to solve the variational equations for the special temperature defined by the crossing of the superconducting dome and the pseudogap transition line. Time reversal symmetry is broken and the weak local magnetic field produced by this inhomogeneous state falls below the threshold of experimental observation. We find that the charge distribution in the layers has an hexadecapole moment in its lowest order.