Competition among various charge-inhomogeneous states and d -wave superconducting state in Hubbard models on square lattices

We study competitions among charge-uniform and -inhomogeneous states in two-dimensional Hubbard models by using a variational Monte Carlo method. At realistic parameters for cuprate superconductors, emergent effective attraction of carriers generated from repulsive Coulomb interaction leads to charge/spin stripe ground states, which severely compete with uniform superconducting excited states in the energy scale of 10 K for cuprates. Stripe period increases with decreasing hole doping δ, which agrees with the experiments for La-based cuprates at δ=1/8. For lower δ, we find a phase separation. Implications of the emergent attraction for cuprates are discussed.