Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards quantitative theory

TL;DR

This review discusses how various theoretical approaches to the two-dimensional Hubbard model successfully explain high-temperature superconductivity and pseudogap phenomena, aligning well with experimental observations in cuprates.

Contribution

It demonstrates that the Hubbard model can quantitatively reproduce key features of high-temperature superconductors, including d-wave pairing, antiferromagnetism, and pseudogap behavior.

Findings

Hubbard model exhibits d-wave superconductivity and antiferromagnetism consistent with experiments.

The pseudogap phenomenon naturally emerges from the model calculations.

Predicted pseudogap temperature matches recent photoemission measurements.

Abstract

This is a short review of the theoretical work on the two-dimensional Hubbard model performed in Sherbrooke in the last few years. It is written on the occasion of the twentieth anniversary of the discovery of high-temperature superconductivity. We discuss several approaches, how they were benchmarked and how they agree sufficiently with each other that we can trust that the results are accurate solutions of the Hubbard model. Then comparisons are made with experiment. We show that the Hubbard model does exhibit d-wave superconductivity and antiferromagnetism essentially where they are observed for both hole and electron-doped cuprates. We also show that the pseudogap phenomenon comes out of these calculations. In the case of electron-doped high temperature superconductors, comparisons with angle-resolved photoemission experiments are nearly quantitative. The value of the pseudogap temperature observed for these compounds in recent photoemission experiments has been predicted by theory before it was observed experimentally. Additional experimental confirmation would be useful. The theoretical methods that are surveyed include mostly the Two-Particle Self-Consistent Approach, Variational Cluster Perturbation Theory (or variational cluster approximation), and Cellular Dynamical Mean-Field Theory.