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We discuss the effects of quenched disorder on a model of charge density wave(CDW) ordering on the square lattice. Our model may be applicable to thecuprate superconductors, where a random electrostatic potential exists in theCuO2 planes as a result of the presence of charged dopants. We argue that thepresence of a random potential can affect the unidirectionality of the CDWorder, characterized by an Ising order parameter. Coupling to a unidirectionalCDW, the random potential can lead to the formation of domains with 90 degreerelative orientation, thus tending to restore the rotational symmetry of theunderlying lattice. We find that the correlation length of the Ising order canbe significantly larger than the CDW correlation length. For a checkerboard CDWon the other hand, disorder generates spatial anisotropies on short lengthscales and thus some degree of unidirectionality. We quantify these disordereffects and suggest new techniques for analyzing the local density of states(LDOS) data measured in scanning tunneling microscopy experiments.Comment: 10 pages, 11 figures; added referenc

From stripe to checkerboard ordering of charge-density waves on the square lattice in the presence of quenched disorder