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

Motivated by the recent experimental determination of the 3D Fermi surface of overdoped La‐based cuprate superconductors, the tight‐binding parameterization of their conduction band is revisited. A minimal tight‐binding model entailing eight orbitals, two of them involving apical oxygen ions is constructed. Parameter optimization allows to almost perfectly reproduce the 3D conduction band as obtained from density functional theory (DFT). It is discussed how each parameter entering this multiband model influences it, and show that the peculiar form of its dispersion severely constraints the parameter values. It is evidenced 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 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. The derivation of a 3D one‐band tight‐binding Hamiltonian for Lanthanum‐based superconducting cuprates is described. It is shown that, in contrast to its purely 2D counterpart, it offers a natural explanation of the recently observed staggering of small and large pieces of the Fermi surface of overdoped La2CuO4 in the basal plane.