AI 中文总结
本文探究Ngai双声子配对机制能否解释掺杂STO的超导电性，计算双声子形变势，推导有效电子-电子相互作用，发现相空间会降低有效耦合，理论预测Tc随掺杂单调增加但与实验不符，确定该机制在其他材料中有效条件并讨论候选材料。
AI 中文摘要
我们探究Ngai提出的双声子配对机制能否解释掺杂钛酸锶（STO）的超导电性。基于第一性原理计算的两种不同理论估计方法，以及基于实验数据的两种经验估计方法，我们对双声子形变势进行了计算，得到了量级完全相同的极大值。我们推导了由双声子交换介导的有效电子-电子相互作用，计算的关键在于所涉及的软声子的强色散特性。由于双声子相互作用的尺度远大于费米能量，Migdal定理不适用。我们得到了可在弱耦合极限下求解的单圈Eliashberg方程。我们发现，尽管电子-声子矩阵元素显著，但相空间因素会大幅降低有效耦合强度。基于临界温度（Tc）的大小，无法排除双声子机制的可能性，但Tc的值由高频物理主导，受软声子行为的影响微弱。该理论预测Tc随掺杂量单调增加，这与实验结果不符。我们确定了双声子机制在其他材料中有效所需的条件，并讨论了可能的候选材料。
英文摘要
We explore the possibility that the two-phonon pairing mechanism proposed by Ngai can explain superconductivity in doped strontium titanate (STO). The two-phonon deformation potential is evaluated using two distinct theoretical estimates based on first-principles calculations and two empirical estimates based on experimental data, yielding very large values of the same order of magnitude. We derive the effective electron-electron interaction mediated by two-phonon exchange. Crucial to our computations is the strong dispersion of the involved soft phonons. Because the scale of the two-phonon interaction is much larger than the Fermi energy, the Migdal theorem does not apply. We obtain a one-loop Eliashberg equation that can be solved in the weak-coupling limit. We find that despite the significant electron-phonon matrix element, phase space considerations considerably reduce the effective coupling. A two-phonon mechanism can not be excluded based on the $T_c$ magnitude, but its value is dominated by the high-energy-frequency physics and is weakly affected by the soft-phonon behavior. The theory predicts a $T_c$ that monotonously increases with doping, which is not in accordance with the experiment. We identify the conditions for a two-phonon mechanism to be effective in other materials and discuss possible candidates.
