Effective Hamiltonian for transition-metal compounds: Application to NaxCoO2

A. A. ALIGIA; T. KROLL

PHYSICAL REVIEW B

AMER PHYSICAL SOC

Lugar: New York; Año: 2010 vol. 81 p. 19 - 5113

1098-0121

We describe a simple scheme to construct a low-energy effective Hamiltonian Heff for highly correlatedsystems containing nonmetals such as O, P, or As ͑O in what follows͒ and a transition-metal ͑M͒ as the activepart in the electronic structure, eliminating the O degrees of freedom from a starting Hamiltonian that containsall M d orbitals and all nonmetal p orbitals. We calculate all interaction terms between d electrons originatingfrom Coulomb repulsion, as a function of three parameters ͑F0, F2, and F4͒ and write them in a basis of orbitalsappropriate for cubic, tetragonal, tetrahedral, or hexagonal symmetry around M. The approach is based onsolving exactly ͑numerically if necessary͒ a MOn cluster containing the transition-metal atom and its n nearestO atoms ͑for example, a CoO6 cluster in the case of the cobaltates, or a CuOn cluster in the case of thecuprates, in which n depends on the number of apical O atoms͒, and mapping them into many-body states ofthe same symmetry containing d holes only. We illustrate the procedure for the case of NaxCoO2. The resultingHeff, including a trigonal distortion D, has been studied recently and its electronic structure agrees well withangle-resolved photoemission spectra ͓A. Bourgeois, A. A. Aligia, and M. J. Rozenberg, Phys. Rev. Lett. 102,066402 ͑2009͔͒. Although Heff contains only 3d t2g holes, the highly correlated states that they representcontain an important amount not only of O 2p holes but also of 3d eg holes. When more holes are added, asignificant redistribution of charge takes place. As a consequence of these facts, the resulting values of theeffective interactions between t2g states are smaller than previously assumed, rendering more important theeffect of D in obtaining only one sheet around the center of the Brillouin zone for the Fermi surface ͑withoutadditional pockets͒.