Theory of Unconventional Superconductivity in Strongly Correlated Systems: Real Space Pairing and Statistically Consistent Mean-Field Theory - in Perspective

TL;DR

This paper reviews real space pairing mechanisms in strongly correlated systems, emphasizing a statistically consistent mean-field approach, phase diagrams, and the distinction between different superconductivity sources, highlighting recent theoretical advances.

Contribution

It introduces a novel, slave-boson-free mean-field theory for real space pairing in strongly correlated superconductors, with comprehensive phase diagrams and conceptual insights.

Findings

Phase diagrams showing stable magnetic and superconducting states.

Real space pairing driven by short-range exchange interaction J.

Distinction between real-space and paramagnon-mediated superconductivity.

Abstract

In this brief overview we discuss the principal features of real space pairing as expressed via corresponding low-energy (t-J or periodic Anderson-Kondo) effective Hamiltonian, as well as consider concrete properties of those unconventional superconductors. We also rise the basic question of statistical consistency within the so-called renormalized mean-field theory. In particular, we provide the phase diagrams encompassing the stable magnetic and superconducting states. We interpret real space pairing as correlated motion of fermion pair coupled by short-range exchange interaction of magnitude J comparable to the particle renormalized band energy $\sim tx$, where $x$ is the carrier number per site. We also discuss briefly the difference between the real-space and the paramagnon - mediated sources of superconductivity. The paper concentrates both on recent novel results obtained in our research group, as well as puts the theoretical concepts in a conceptual as well as historical perspective. No slave-bosons are required to formulate the present approach.