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 neighbor hopping ($t'$). When $|t'/t|$ is small, as appropriate for ${ \rm La_{ 2-x}Sr_xCuO_4}$, stripes are found, whereas in compounds with larger $|t'/t|$ (such as ${ \rm Ca_{ 2-x}Na_x CuO_2Cl_2}$ and ${ \rm Bi_2Sr_2CaCu_2O_{ 8+\delta}}$) 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.
Categories: cond-mat.str-el cond-mat.supr-con