Competition among various charge-inhomogeneous states and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-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 $\ensuremath{\delta}$, which agrees with the experiments for La-based cuprates at $\ensuremath{\delta}=1/8$. For lower $\ensuremath{\delta}$, we find a phase separation. Implications of the emergent attraction for cuprates are discussed.

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