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Physica B Condensed Matter

Raman scattering in the two-dimensional Hubbard model

Takami Tohyama, Jun-ichiro Inoue, Sadamichi Maekawa

Published May 1, 1993• 1 citation
Publisher
DOI
10.1016/0921-4526(93)90759-y

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Cluster dynamical mean field methods are used to calculate the superconductivity-induced changes in the interplane conductivity and Raman scattering cross section of the two-dimensional Hubbard model. When superconductivity emerges from the pseudogap, the superconducting response is found to be diminished in amplitude, broadened, and, in the case of the interplane conductivity, shifted to higher frequency. The results are in agreement with data on high-temperature copper-oxide superconductors indicating that the Hubbard model contains the essential low-energy physics of the pseudogap and its interplay with superconductivity in the cuprates.
We investigate the resonant two-magnon Raman scattering in two-dimensional (2D) Mott insulators by using a half-filled 2D Hubbard model in the strong coupling limit. By performing numerical diagonalization calculations for small clusters, we find that the Raman intensity is enhanced when the incoming photon energy is not near the optical absorption edge but well above it, being consistent with experimental data. The absence of resonance near the gap edge is associated with the presence of background spins, while photoexcited states for resonance are found to be characterized by the charge degree of freedom. The resonance mechanism is different from those proposed previously.
Symmetry of photoexcited states with two photoinduced carriers in two-dimensional Mott insulators is examined by applying the numerically exact diagonalization method to finite-size clusters of a half-filled Hubbard model in the strong-coupling limit. The symmetry of minimum-energy bound state is found to be s-wave, which is different from a d_{x^2-y^2} wave of a two-hole pair in doped Mott insulators. We demonstrate that the difference is originated from an exchange of fermions due to the motion of a doubly occupied site. Correspondingly large-shift Raman scattering across the Mott gap exhibits a minimum-energy excitation in the A1 (s-wave) channel. We discuss implications of the results for the Raman scattering and other optical experiments.