A 3D Tight-Binding Model for La-Based Cuprate Superconductors

TL;DR

This paper develops a detailed three-dimensional tight-binding model for overdoped La-based cuprate superconductors, accurately reproducing their conduction band and Fermi surface as observed experimentally and via DFT.

Contribution

It introduces an eight-orbital tight-binding model that captures the 3D electronic structure and clarifies the microscopical origins of hopping parameters, improving upon existing models.

Findings

The model closely matches DFT conduction bands.

Standard perturbation methods poorly converge due to small charge transfer gap.

Including longer-range hoppings preserves agreement with DFT and experimental Fermi surface.

Abstract

Motivated by the recent experimental determination of the three-dimensional Fermi surface of overdoped La-based cuprate superconductors [Horio et al., Phys. Rev. Lett. 2018, 121, 077004], we revisit the tight-binding parameterization of their conduction band. We construct a minimal tight-binding model entailing eight orbitals, two of them involving apical oxygen ions. Parameter optimization allows to almost perfectly reproduce the three-dimensional conduction band as obtained from density functional theory (DFT). We discuss how each parameter entering this multiband model influences it, and show that the peculiar form of its dispersion severely constraints the parameter values. We then evidence that standard perturbative derivation of an effective one-band model is poorly converging because of the comparatively small value of the charge transfer gap. Yet, this allows us to unravel the microscopical origin of the in-plane and out-of-plane hopping amplitudes. An alternative approach to the computation of the tight-binding parameters of the effective model is presented and worked out. It results that the agreement with DFT is preserved provided longer-ranged hopping amplitudes are retained. A comparison with existing models is also performed. Finally, the Fermi surface, showing staggered pieces alternating in size and shape, is compared to experiment, with the density of states also being calculated.