Phase separation and competition of superconductivity and magnetism in the two-dimensional Hubbard model: From strong to weak coupling

摘要

Cooperation and competition between the antiferromagnetic, d-wavesuperconducting and Mott-insulating states are explored for the two-dimensionalHubbard model including nearest and next-nearest-neighbor hoppings at zerotemperature. Using the variational cluster approach with clusters of differentshapes and sizes up to 10 sites, it is found that the doping-driven transitionfrom a phase with microscopic coexistence of antiferromagnetism andsuperconductivity to a purely superconducting phase is discontinuous for stronginteraction and accompanied by phase separation. At half-filling the system isin an antiferromagnetic Mott-insulating state with vanishing chargecompressibility. Upon decreasing the interaction strength U below a certaincritical value of roughly U=4 (in units of the nearest-neighbor hopping),however, the filling-dependent magnetic transition changes its character andbecomes continuous. Phase separation or, more carefully, the tendency towardsthe formation of inhomogeneous states disappears. This critical value is incontrast to previous studies, where a much larger value was obtained. Moreover,we find that the system at half-filling undergoes the Mott transition from aninsulator to a state with a finite charge compressibility at essentially thesame value. The weakly correlated state at half-filling exhibitssuperconductivity microscopically admixed to the antiferromagnetic order. Thisscenario suggests a close relation between phase separation and theMott-insulator physics.