  We perform variational Monte Carlo simulations of the single-band Hubbard
model on the square lattice with both nearest ($t$) and next-nearest ($t'$)
neighbor hoppings. Our work investigates the consequences of increasing hole
doping on the instauration of stripes and the behavior of the superconducting
order parameter, with a discussion on how the two phenomena affect each other.
We consider two different values of the next-nearest neighbor hopping
parameter, that are appropriate for describing cuprate superconductors. We
observe that stripes are the optimal state in a wide doping range; the stripe
wavelength reduces at increasing doping, until stripes melt into a uniform
state for large values of doping. Superconducting pair-pair correlations,
indicating the presence of superconductivity, are always suppressed in the
presence of stripes. Our results suggest that the phase diagram for the
single-band Hubbard model is dominated by stripes, with superconductivity being
possible only in a narrow doping range between striped states and a
nonsuperconducting metal.
