The combined effect of a lateral square superlattice potential and the Coulomb interaction on the ground state of a two-dimensional electron gas in a perpendicular magnetic field is studied for different rational values of Γ, the inverse of the number of flux quanta per unit cell of the external potential, at filling factor ν = 1 in Landau level N = 0. When Landau level mixing and disorder effects are neglected, increasing the strength W0 of the potential induces a transition, at a critical strength W (c) 0 , from a uniform and fully spin polarized state to a two-dimensional charge density wave (CDW) with a meronlike spin texture at each maximum and minimum of the CDW. The collective excitations of this "vortex-CDW" are similar to those of the Skyrme crystal that is expected to be the ground state near filling factor ν = 1. In particular, a broken U(1) symmetry in the vortex-CDW results in an extra gapless phase mode that could provide a fast channel for the relaxation of nuclear spins. The average spin polarization Sz changes in a continuous or discontinuous manner as W0 is increased depending on whether Γ ∈ [1/2, 1] or Γ ∈ [0, 1/2] . The phase mode and the meronlike spin texture disappear at large value of W0, leaving as the ground state partially spin-polarized CDW if Γ = 1/2 or a spin-unpolarized CDW if Γ = 1/2.
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