Optical, magnetic, and single-particle excitations in the multiband Hubbard model for cuprate superconductors

Abstract

On the basis of exact diagonalizations, a comparative study of two-particle optical and magnetic, as well as single-particle, excitations is presented for a two-dimensional (2D) multiorbital Hubbard model. For reasonable parameter sets appropriate for the cuprate superconductors, the single-particle excitations display strongly correlated states related to the Zhang-Rice Cu-O singlet construction. These states define the gap (to the upper Hubbard band) at half-filling and become partially occupied by doping holes in our 2×2 unit-cell system. The optical results, which are the first quantitative calculations performed for realistic parameters of the three-band Hubbard model, clearly show three allowed optical transitions: (i) itinerant motion of the Cu-O singlets, having (for doping concentrations x≠0) a spectral Drude distribution around ω=0 with spectral weight proportional to x; (ii) unbinding of the O hole from the Cu spin in the singlet. This gives, in particular, a strong absorption peak due to singlet→nonbonding oxygen transitions, again with relative weight ∼x. It is roughly centered at ω∼JKondo<Δ, where JKondo is the Kondo coupling and Δ the bare Cu-O charge-transfer energy. It is this singlet unbinding that results in the by far dominant absorption structure between Drude and higher-energy Cu-O transitions and not the often discussed ‘‘mid-infrared’’ absorption due to transitions between different singlet states. (iii) Cu-O charge-transfer processes at energy ∼Δ+Upd. They show a pronounced excitonic effect due to the p-d interaction Upd and have a reduced spectral weight shifted to higher energies for increased dopings. Findings (i)–(iii) are in general accordance with recent experimental data. Our study of the low-energy absorption is complemented with a numerical scaling analysis of the Drude weight in 1D, where, in particular, we find an interesting violation of Lenz’s law for 4n-site Hubbard rings. Finally, the magnetic structure factor is calculated for the 2D case. For finite doping it contains a peak at 2JKondo, which should be detectable in experiment.

Similar papers