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By using the local-density approximation + dynamical mean field theory method, we show that the Coulomb anisotropy and the correlation-enhanced spin-orbit coupling play a crucial role in determining the Fermi surface of Sr2RuO4.We also find a strong spin-orbital entanglement.This suggests that the conventional description of Cooper pairs via factorized spin and orbital two-particle functions might not apply to Sr2RuO4.