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

Abstract

With high-Tc cuprates in mind, properties of correlated dx2-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 to describe
correlated SC and normal states as doped Mott insulators. U/t, t'/t and \delta
(doping rate) dependence of relevant quantities are systematically calculated.
As U/t increases, a sharp crossover of SC properties occurs at U_co/t \sim 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\lsim 5, steady superconductivity corresponding to the
cuprates is not found, whereas the d-wave SC correlation function Pd^\infty
rapidly increases for U/t\gsim 6 and becomes maximum at U=U_co. Comparing the
\delta dependence of Pd^\infty with experimentally observed dome-shaped Tc and
condensation energy, we find that the effective value of $U$ for the cuprates
should be larger than the band width, 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 a proper 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.