Interplay between incommensurate phases in the cuprates

We establish the qualitative behavior of the incommensurability $ϵ$, optimal domain wall filling $\nu$ and chemical potential $\mu$ for increasing doping by a systematic slave-boson study of an array of vertical stripes separated by up to $d=11$ lattice constants. Our findings obtained in the Hubbard model with the next-nearest neighbor hopping $t^{\mathrm{\prime }}=-0.15t$ agree qualitatively with the experimental data for the cuprates in the doping regime $x\lesssim 1\mathrm{/}8$. It is found that $t^{\mathrm{\prime }}$ modifies the optimal filling $\nu$ and triggers the crossover to the diagonal (1,1) spiral phase at increasing doping, stabilized already at $x\simeq 0.09$ for $t^{\mathrm{\prime }}=-0.3t$.