The isotope coefficient of the pseudogap in high-Tc superconductors

In the Letter, we present the theory of the phonon-induced spin density waves (SDW) for two-dimensional electron system. In our considerations two-dimensional materials are modeled by the logarithmic singularity in the density of states. The SDW gap is identified as the pseudogap (PG) in the energy spectrum of underdoped superconductors. In the Letter, we construct the Eliashberg equations for spin density waves, derive analytically the expression for the SDW transition temperature TSDW and the adequately isotope coefficient αSDW. We show that the strong-coupling SDW theory can explain qualitatively the experimental features, such as the large values of the pseudogap critical temperature T∗ and the small value of the pseudogap isotope coefficient α∗, despite the fact that SDW originates from pure electron-phonon interaction. However, the strong Coulomb correlations play more important role in the cuprates and must be included in the complete quantitative analysis.