Symmetry of the charge density wave in cuprates

We derive and analyze an effective Ginzburg-Landau (GL) functional for a charge density wave (CDW) for a model of electrons on a tight binding square lattice with density-density interactions. We show, using realistic electronic dispersions for the cuprates, that for the simplest GL theory, the preferred symmetry is of the uni-directional (stripe) type, but upon inclusion of third-order terms, the CDW may exhibit a transition from a uni-directional to a checkerboard pattern depending on the strength and range of the interaction.