Microscopic theory of a high T _c cuprate Bi ₂ Sr ₂ CaCu ₂ O _8+x based on main pairing channel of electrons in CuO planes due to 40mev lateral vibrations of the apical oxygen atoms in adjacent the SrO ionic insulator layer is proposed. The separation between the vibrating charged atoms and the 2D electron gas creates the forward scattering peak leading in turn to the d -wave pairing within Eliashberg formalism. The phonon mode naturally explain the kink in dispersion relation observed by ARPES and the and effect of the O ¹⁶ → O ¹⁸ isotope substitution in the normal state. To describe the pseudogap physics a single band fourfold symmetric Hubbard model, with the hopping parameters and the on site repulsion e U ∼ 6t. It described the Mott insulator at low doping, while at higher dopping the pseudogap physics (still strongly correlated) can be be approximated by the symmetrized mean field model and with renormalized U incorporating screening. The location of the transition line T ^*between the locally antiferromagnetic pseudogap and the paramagnetic overdoped phases and susceptibility (describing spin fluctuations coupling to 2DEG) are also obtained within this approximation. The superconducting d - wave gap mainly due to the phonon channel but is assisted by the spin fluctuations (15%–20%). The dependence of the gap and T _c on doping and effect of the isotope substitution are obtained and is consistent with experiments.

提出了高T _c铜酸盐Bi ₂ Sr ₂ CaCu ₂ O _{8+ x}的微观理论，该理论基于CuO平面中电子的主要配对通道，这是由于与SrO离子绝缘体层相邻的顶端氧原子的40 mev横向振动。振动的带电原子和二维电子气之间的分离产生了前向散射峰，进而导致了 Eliashberg 形式主义中的 d 波配对。声子模式自然地解释了 ARPES 观察到的色散关系的扭结以及O ¹⁶ → O ^{18 的影响} 正常状态下的同位素取代。为了描述赝隙物理，使用单带四重对称哈伯德模型，具有跳跃参数和现场排斥 e U ∼ 6 t。它描述了低掺杂的莫特绝缘体，而在高掺杂时，赝隙物理（仍然强相关）可以通过对称平均场模型和包含屏蔽的重归一化U来近似。局部反铁磁赝隙和顺磁过掺杂相和磁化率（描述耦合到 2DEG 的自旋波动）之间的过渡线T ^*的位置也在该近似中获得。超导d- 波隙主要是由于声子通道，但由自旋波动 (15%–20%) 辅助。获得了间隙和T _c对掺杂和同位素取代效应的依赖性并且与实验一致。