LDA energy bands, low-energy Hamiltonians, t', t'', t_{perp}(k), and J_{perp}

TL;DR

This paper analyzes the electronic bandstructure of YBa2Cu3O7 using LDA calculations, deriving simplified Hamiltonians and emphasizing the importance of specific hopping parameters for understanding experimental data and magnetic interactions.

Contribution

It provides a detailed derivation of multi-band Hamiltonians from LDA results, highlighting the roles of various orbitals and hopping terms in cuprate superconductors.

Findings

Derived 8-band Hamiltonians for bilayer cuprates.

Showed the importance of t' for ARPES in Sr2CuO2Cl2.

Estimated inter-plane exchange constants using different Hamiltonians.

Abstract

We describe the LDA bandstructure of YBa_2Cu_3O_7 in the 2 eV range from the Fermi energy using orbital projections and compare with YBa_2Cu_4O_8. Then, the high-energy and chain-related degrees of freedom are integrated out and we arrive at two, nearest-neighbor, orthogonal, two-center, 8-band Hamiltonians, the even and odd bands of the bi-layer. Of the 8 orbitals, Cu{x2-y2}, O2x, O3y, and Cus have \sigma character and Cu{xz}, Cu{yz} O2z, and O3z have \pi character. The roles of the Cu_s orbital, which has some Cu{3z2-1} character, and the four \pi orbitals are as follows: Cu_s provides 2nd- and 3rd-nearest-neighbor (t' and t') intra-plane hopping, as well as hopping between planes (t_{perp}). The \pi -orbitals are responsible for bifurcation of the saddle-points for dimpled planes. The 4-\sigma-band Hamiltonian is generic for flat CuO_2 planes and we use it for analytical studies. The reduction of the \sigma-Hamiltonian to 3- and 1-band Hamiltonians is explicitly discussed and we point out that, in addition to the hoppings commonly included in many-body calculations, the 3-band Hamiltonian should include hopping between all 2nd-nearest-neighbor oxygens and that the 1-band Hamiltonian should include 3rd-nearest-neighbor hoppings. We calculate the single-particle hopping between the planes of a bi-layer. We show that the inclusion of t' is crucial for understanding ARPES for the anti-ferromagnetic insulator Sr_2CuO_2Cl_2. Finally, we estimate the value of the inter-plane exchange constant for an un-doped bi-layer in mean-field theory using different single-particle Hamiltonians.