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

Abstract

With high-Tc cuprates in mind, the properties of correlated d x 2 −y 2 -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 δ (doping rate) dependences of relevant quantities are systematically calculated. As U/t increases, a sharp crossover of SC properties occurs at Uco/t ∼ 10 from a conventional BCS type to a kinetic-energy-driven type for any t ′ /t. As δ decreases, Uco/t is smoothly connected to the Mott transition point at half filling. For U/t < ∼ 5, steady superconductivity corresponding to the cuprates is not found, whereas the d-wave SC correlation function P ∞ d rapidly increases for U/t > ∼ 6 and becomes maximum at U = Uco. Comparing the δ dependence of P ∞ d with an experimentally observed dome-shaped Tc 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 > Uco, only doped holes (electrons) become charge carriers, which will make a small Fermi surface (hole pocket), but for U < Uco 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 > Uco 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.

Staggered Flux State in Two-Dimensional Hubbard Models

“…It has been shown that, in a wide range of the parameter space of concern, a d-SC state becomes stable compared with the projected Fermi sea (ordinary normal state). 35 …”

Effect of Diagonal Hopping on Staggered Flux State in Square-Lattice Hubbard model

“…Here, P G is the fundamental onsite (Gutzwiller) projection, and P Q is a nearest-neighbor doublon-holon projection, which is indispensable for Mott physics [13,14]:…”

“…Main properties of these states have been already studied for eq. (1) [14,15]. Here, we do not introduce the band renormalization effect into the optimization, but for Ψ N , we can substantially allow for this effect within t , as will be explained in sec.…”

“…Note that ∆E SF is sizable in a strongly correlated regime, although it is always smaller than ∆E d . The AF state is the most stable because of the nesting condition, but Ψ AF becomes unstable against phase separation for δ > 0 and t /t 0 [14]. Because the AF state is unlikely to be the normal state that yields SC, we do not treat Ψ AF further.…”

“…2. At half filling, E/t is symmetric with respect to t /t = 0, owing to the electron-hole symmetry [14]. First, we consider E(N).…”