High Temperature Superconductivity in the Cuprates: Phenomena from a Theorist's Point of View

TL;DR

This paper reviews experimental findings on cuprate superconductors, focusing on the strange metal state and pseudogap phenomena, and discusses correlations and initial theoretical insights into their strongly correlated nature.

Contribution

It provides a comprehensive overview of experimental phenomena in cuprates and outlines initial theoretical steps towards understanding their strongly correlated electronic states.

Findings

Correlation between $T_c$ and superfluid density

Linear resistivity correlates with $T_c$

Empirical relations suggest underlying strongly correlated physics

Abstract

I present a selection of experimental results on metallic cuprates, both above the superconducting transition temperature $T_c$ (often called the strange metal state) and in the superconducting state. It highlights this still poorly understood part of the physical world. After an introduction, I talk briefly about the pseudogap regime and about the unusual linear resistivity phenomenon. Several empirical correlations between observed quantities are mentioned, e.g. $T_c$ and superfluid density (Uemura), $T_c$ and next nearest neighbour hopping, slope of the linear resistivity and $T_c$. In the belief that a comprehensive explanation may need an understanding of the extremely strongly correlated metal, a few initial steps in this direction are outlined.