Superconductivity in optimally doped Cuprates: BZA Program works well & Superexchange is the Glue

TL;DR

This paper reviews the development of the BZA program, which provided a microscopic understanding of superconductivity in optimally doped cuprates through resonating valence bond states and superexchange interactions.

Contribution

It highlights the foundational role of BZA and gauge theory approaches in explaining unconventional superconductivity and related phenomena in cuprates.

Findings

BZA theory successfully explains d-wave superconductivity

Gauge theory approaches extend understanding of RVB states

BZA work underpins subsequent developments in cuprate physics

Abstract

Resonating valence bond states in a doped Mott insulator was proposed to explain superconductivity in cuprates in January 1987 by Anderson. A challenging task then was proving existence of this unconventional mechanism and a wealth of possibilities, with a rigor acceptable in standard condensed matter physics, in a microscopic theory and develop suitable many body techniques. Shortly, a paper by Anderson, Zou and us (BZA) undertook this task and initiated a program. Three key papers that followed, shortly, essentially completed the program, as far as superconductivity is concerned: i) a gauge theory approach by Anderson and us, that went beyond mean field theory ii) Kotliar's d-wave solution in BZA theory iii) improvement of a renormalized Hamiltonian in BZA theory, using a Gutzwiller approximation by Zhang, Gros, Rice and Shiba. In this article I shall focus on the merits of BZA and gauge theory papers. They turned out to be a foundation for subsequent developments dealing with more aspects that were unconventional - d-wave order parameter with nodal Bogoliubov quasi particles, Affleck-Marston's $\pi$-flux condensed spin liquid phase, unconventional spin-1 collective mode at $(\pi,\pi)$, and other fascinating developments. Kivelson, Rokhsar and Sethna's idea of holons and their bose condensation found expression in the slave boson formalism and lead to results similar to BZA program. Further, t-J model is a good minimal model around optimal doping, where RVB superconductivity is also at its best.