Crossover between BCS Superconductor and Doped Mott Insulator of d-Wave Pairing State in Two-Dimensional Hubbard Model

With high-T-c cuprates in mind, the properties of correlated d(x2-y2)-wave superconducting (SC) and antiferromagnetic (AF) states are studied for the Hubbard (t-t'-U) model on square lattices using a variational Monte Carlo method. We employ simple trial wave functions including only crucial parameters, such as a doublon-holon binding factor indispensable for describing correlated SC and normal states as doped Mott insulators. The U/t, t'/t, and delta (doping rate) dependences of relevant quantities are systematically calculated. As U/t increases, a sharp crossover of SC properties occurs at U-co/t similar to 10 from a conventional BCS type to a kinetic-energy-driven type for any t'/t. As delta decreases, U-co/t is smoothly connected to the Mott transition point at half filling. For U/t less than or similar to 5, steady superconductivity corresponding to the cuprates is not found, whereas the d-wave SC correlation function P-d(infinity) rapidly increases for U/t greater than or similar to 6 and becomes maximum at U = U-co. Comparing the delta dependence of P-d(delta) with an experimentally observed dome-shaped T-c and condensation energy, we find that the effective value of U for cuprates should be larger than the bandwidth, for which the t-J model is valid. Analyzing the kinetic energy, we reveal that, for U > U-co, only doped holes (electrons) become charge carriers, which will make a small Fermi surface (hole pocket), but for U < U-co all the electrons (holes) contribute to conduction and will make an ordinary large Fermi surface, which is contradictory to the feature of cuprates. By introducing an appropriate negative (positive) t'/t, the SC (AF) state is stabilized. In the underdoped regime, the strength of SC for U > U-co is determined by two factors, i.e., the AF spin correlation, which creates singlet pairs (pseudogap), and the charge mobility dominated by Mott physics. In this connection, we argue that the electrons near the antinodal points in the momentum space play a leading role in stabilizing the d-wave state, in contrast to the dichotomy of electronic roles in the momentum space proposed for the two-gap problem. We also show the instability of the hole-doped AF state against phase separation.