Checkerboard and stripe inhomogeneities in cuprates

We systematically investigate charge-ordering phases by means of a restricted and unrestricted Gutzwiller approximation to the single-band Hubbard model with nearest- (t) and next-nearest- (t(')) neighbor hopping. When parallel to t(')/t parallel to is small, as appropriate for La2-xSrxCuO4, stripes are found, whereas in compounds with larger parallel to t(')/t parallel to (such as Ca2-xNaxCuO2Cl2 and Bi2Sr2CaCu2O8+delta) checkerboard structures are favored. In contrast to the linear doping dependence found for stripes the charge periodicity of checkerboard textures is locked to 4 unit cells over a wide doping range. In addition we find that checkerboard structures are favored at surfaces.