High-temperature superconductivity in the Hubbard model: Gutzwiller wave-function solution

TL;DR

This paper introduces a new diagrammatic method for analyzing superconductivity in the 2D Hubbard model, revealing key features like the doping dependence of the gap and Fermi velocity, aligning well with experimental data on cuprates.

Contribution

The paper develops a systematic diagrammatic expansion for Gutzwiller wave functions to study superconductivity in the Hubbard model, providing detailed phase diagrams and physical insights.

Findings

Superconductivity appears for U/t > 3 and doping < 0.32.

The SC gap resembles d_{x^2-y^2} wave near optimal doping.

The nodal Fermi velocity remains nearly constant across doping levels.

Abstract

A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes t (and t') between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters (U, \delta, t') and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, U/t > 3, and for not too large hole doping, \delta < 0.32 for t' = 0.25 t; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles $d_{x^2-y^2}$-wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.