Van Hove Exciton-Cageons and High-T$_c$ Superconductivity, XA: Role of Spin-Orbit Coupling in Generating a Diabolical Point

TL;DR

This paper investigates how spin-orbit coupling influences the electronic structure of La$_{2-x}$Sr$_x$CuO$_4$, revealing the formation of diabolical points and the effects of strong correlations near the metal-insulator transition.

Contribution

It provides a detailed analysis of the impact of spin-orbit coupling on van Hove singularities and Fermi surfaces, including a slave boson approach and an analytical crossover near the transition.

Findings

Spin-orbit coupling splits van Hove singularities.

Fermi surface shape is significantly altered by SOC.

Near the metal-insulator transition, a scaling regime allows analytical insights.

Abstract

Spin-orbit coupling plays a large role in stabilizing the low-temperature orthorhombic phase of La$_{2-x}$Sr$_x$CuO$_4$. It splits the degeneracy of the van Hove singularities (thereby stabilizing the distorted phase) and completely changes the shape of the Fermi surfaces, potentially introducing diabolical points into the band structure. The present paper gives a detailed account of the resulting electronic structure. A slave boson calculation shows how these results are modified in the presence of strong correlation effects. A scaling regime, found very close to the metal-insulator transition, allows an analytical determination of the crossover, in the limit of zero oxygen-oxygen hopping, $t_{OO}\rightarrow 0$. Extreme care must exercised in chosing the parameters of the three-band model. In particular, $t_{OO}$ is renormalized from its LDA value. Furthermore, it is suggested that the slave boson model be spin-corrected, in which case the system is close to a metal-insulator transition at half filling.