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

TL;DR

This study investigates the crossover in superconducting properties of the two-dimensional Hubbard model, revealing a transition from BCS-like to kinetic-energy-driven pairing as interaction strength increases, with implications for cuprate superconductors.

Contribution

It identifies a sharp crossover at U/t ~ 10 from BCS to kinetic-energy-driven superconductivity and links this to the physics of doped Mott insulators in cuprates.

Findings

Superconductivity emerges for U/t > 6, peaking at U=U_co.

The effective U in cuprates exceeds the band width, challenging the t-J model.

Charge carriers switch from electrons to holes across the crossover.

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.