Competing and Cooperative Effects of Spin, Charge, and Phonon Degrees of Freedom in HTSC

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The phase diagram of high-Tc superconducting copper oxides (HTSC) exhibits an unusual complexity which is, at present, beyond any microscopic modeling. Motivated by very recent experimental findings—(i) a giant isotope effect on T* and (ii) doping-dependent phonon anomalies and “extra” modes—the role played by the lattice is reinvestigated and the consequences arising for the striped phase are discussed. By including nonlinear higher-order phonon–phonon and density–density interactions in the Hamiltonian, an isotope effect on T* is obtained, as well as substantial q-dependent phonon anomalies, where both effects are strongly doping dependent.